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Academic literature on the topic 'Spanning graphs of hypercubes'

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Published: 4 May 2024

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Journal articles on the topic "Spanning graphs of hypercubes"

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Kobeissi, Mohamed, and Michel Mollard. "Disjoint cycles and spanning graphs of hypercubes." Discrete Mathematics 288, no. 1-3 (November 2004): 73–87. http://dx.doi.org/10.1016/j.disc.2004.08.005.

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Kobeissi, Mohamed, and Michel Mollard. "Spanning graphs of hypercubes: starlike and double starlike trees." Discrete Mathematics 244, no. 1-3 (February 2002): 231–39. http://dx.doi.org/10.1016/s0012-365x(01)00086-3.

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LIN, LAN, and YIXUN LIN. "The Minimum Stretch Spanning Tree Problem for Hamming Graphs and Higher-Dimensional Grids." Journal of Interconnection Networks 20, no. 01 (March 2020): 2050004. http://dx.doi.org/10.1142/s0219265920500048.

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The minimum stretch spanning tree problem for a graph G is to find a spanning tree T of G such that the maximum distance in T between two adjacent vertices is minimized. The minimum value of this optimization problem gives rise to a graph invariant σ(G), called the tree-stretch of G. The problem has been proved NP-hard. In this paper we present a general approach to determine the exact values σ(G) for a series of typical graphs arising from communication networks, such as Hamming graphs and higher-dimensional grids (including hypercubes).
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RIORDAN, OLIVER. "Spanning Subgraphs of Random Graphs." Combinatorics, Probability and Computing 9, no. 2 (March 2000): 125–48. http://dx.doi.org/10.1017/s0963548399004150.

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Let Gp be a random graph on 2d vertices where edges are selected independently with a fixed probability p > ¼, and let H be the d-dimensional hypercube Qd. We answer a question of Bollobás by showing that, as d → ∞, Gp almost surely has a spanning subgraph isomorphic to H. In fact we prove a stronger result which implies that the number of d-cubes in G ∈ [Gscr ](n, M) is asymptotically normally distributed for M in a certain range. The result proved can be applied to many other graphs, also improving previous results for the lattice, that is, the 2-dimensional square grid. The proof uses the second moment method – writing X for the number of subgraphs of G isomorphic to H, where G is a suitable random graph, we expand the variance of X as a sum over all subgraphs of H itself. As the subgraphs of H may be quite complicated, most of the work is in estimating the various terms of this sum.
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YANG, JINN-SHYONG, JOU-MING CHANG, SHYUE-MING TANG, and YUE-LI WANG. "CONSTRUCTING MULTIPLE INDEPENDENT SPANNING TREES ON RECURSIVE CIRCULANT GRAPHS G(2m, 2)." International Journal of Foundations of Computer Science 21, no. 01 (February 2010): 73–90. http://dx.doi.org/10.1142/s0129054110007143.

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A recursive circulant graph G(N,d) has N = cdm vertices labeled from 0 to N - 1, where d ⩾ 2, m ⩾ 1, and 1 ⩽ c < d, and two vertices x,y ∈ G(N,d) are adjacent if and only if there is an integer k with 0 ⩽ k ⩽ ⌈ log d N⌉ - 1 such that x ± dk ≡ y ( mod N). With the aid of recursive structure, such class of graphs has many attractive features and was considered as a topology of interconnection networks for computing systems. The design of multiple independent spanning trees (ISTs) has many applications in network communication. For instance, it is useful for fault-tolerant broadcasting and secure message distribution. In the previous work of Yang et al. (2009), we provided a constructing scheme to build k ISTs on G(cdm,d) with d ⩾ 3, where k is the connectivity of G(cdm,d). However, the proposed constructing rules cannot be applied to the case of d = 2. For the integrity of solving the IST problem on recursive circulant graphs, this paper deals with the case of G(2m,2) using a set of different constructing rules. Especially, we show that the heights of ISTs for G(2m,2) are lower than the known optimal construction of hypercubes with the same number of vertices.
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Tien, Jenn-Yang, and Wei-Pang Yang. "Hierarchical spanning trees and distributing on incomplete hypercubes." Parallel Computing 17, no. 12 (December 1991): 1343–60. http://dx.doi.org/10.1016/s0167-8191(05)80002-x.

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Pai, Kung-Jui. "Dual Protection Routing Trees on Graphs." Mathematics 11, no. 14 (July 24, 2023): 3255. http://dx.doi.org/10.3390/math11143255.

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In IP networks, packet forwarding is destination-based and hop-by-hop, and routes are built as needed. Kwong et al. introduced a protection routing in which packet delivery to the destination node can proceed uninterrupted in the event of any single node or link failure. He then showed that “whether there is a protection routing to the destination” is NP-complete. Tapolcai found that two completely independent spanning trees, abbreviated as CISTs, can be used to configure the protection routing. In this paper, we proposed dual protection routing trees, denoted as dual-PRTs to replace CISTs, which are less restrictive than CISTs. Next, we proposed a transformation algorithm that uses dual-PRTs to configure the protection routing. Taking complete graphs Kn, complete bipartite graphs Km,n, hypercubes Qn, and locally twisted cubes LTQn as examples, we provided a recursive method to construct dual-PRTs on them. This article showed that there are no two CISTs on K3,3, Q3, and LTQ3, but there exist dual-PRTs that can be used to configure the protection routing. As shown in the performance evaluation of simulation results, for both Qn and LTQn, we get the average path length of protection routing configured by dual-PRTs is shorter than that by two CISTs.
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Yang, Jinn-Shyong, Shyue-Ming Tang, Jou-Ming Chang, and Yue-Li Wang. "Parallel construction of optimal independent spanning trees on hypercubes." Parallel Computing 33, no. 1 (February 2007): 73–79. http://dx.doi.org/10.1016/j.parco.2006.12.001.

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Nieminen, Juhani, Matti Peltola, and Pasi Ruotsalainen. "On Graphs Like Hypercubes." Tsukuba Journal of Mathematics 32, no. 1 (June 2008): 37–48. http://dx.doi.org/10.21099/tkbjm/1496165191.

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Locke, Stephen C., and Richard Stong. "Spanning Cycles in Hypercubes: 10892." American Mathematical Monthly 110, no. 5 (May 2003): 440. http://dx.doi.org/10.2307/3647840.

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Dissertations / Theses on the topic "Spanning graphs of hypercubes"

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Kobeissi, Mohamed. "Plongement de graphes dans l'hypercube." Phd thesis, Grenoble 1, 2001. https://theses.hal.science/tel-00004683.

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Le but principal de ce manuscrit est de montrer que certaines familles de graphes sont des graphes plongeables dans l'hypercube. Un problème d'une autre nature sera traité, il concerne la partition de l'hypercube en des cycles sommet-disjoints de longueur paires. Nous prouvons que l'hypercube de dimension n peut être partitionné en k cycles sommet-disjoints si k
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Vasquez, Maria Rosario. "An investigation of super line graphs of hypercubes." Virtual Press, 1993. http://liblink.bsu.edu/uhtbin/catkey/865951.

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Graphs, as mathematical objects, play a dominant role in the study of network modeling, VLSI design, data structures, parallel computation, process scheduling and in a variety of other areas of computer science. Hypercubes are one of the preferred architectures for parallel computation, and a study of some properties of the hypercubes motivated this thesis.The concept of super line graphs, introduced by Bagga at el, generalizes the notion of line graphs. In this thesis several graph theoretic properties of super line graphs of hypercubes are studied. In particular the super line graphs of index two of hypercubes are investigated and some exact results and precise characterizations are found.
Department of Computer Science
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Montgomery, Richard Harford. "Minors and spanning trees in graphs." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709278.

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Knox, Fiachra. "Embedding spanning structures in graphs and hypergraphs." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4027/.

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In this thesis we prove three main results on embeddings of spanning subgraphs into graphs and hypergraphs. The first is that for log⁵⁰ n/n \ ≤ p ≤ 1-n⁻¹/⁴ log⁹ n, a binomial random graph G ~ G_n,p contains with high probability a collection of └δ(G)/2┘ edge disjoint Hamilton cycles (plus an additional edge-disjoint matching if δ(G) is odd), which confirms for this range of p a conjecture of Frieze and Krivelevich. Secondly, we show that any 'robustly expanding' graph with linear minimum degree on sufficiently many vertices contains every bipartite graph on the same number of vertices with bounded maximum degree and sublinear bandwidth. As corollaries we obtain the same result for any graph which satisfies the Ore-type condition d(x) + d(y) ≥ (1 + η)n for non-adjacent vertices x and y, or which satisfies a certain degree sequence condition. Thirdly, for γ > 0 we give a polynomial-time algorithm for determining whether or not a k-graph with minimum codegree at least (1/k + γ)n contains a perfect matching. This essentially answers a question of Rodl, Rucinski and Szemeredi. Our algorithm relies on a strengthening of a structural result of Keevash and Mycroft. Finally and additionally, we include a short note on Maker-Breaker games.
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Mahoney, James Raymond. "Tree Graphs and Orthogonal Spanning Tree Decompositions." PDXScholar, 2016. http://pdxscholar.library.pdx.edu/open_access_etds/2944.

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Given a graph G, we construct T(G), called the tree graph of G. The vertices of T(G) are the spanning trees of G, with edges between vertices when their respective spanning trees differ only by a single edge. In this paper we detail many new results concerning tree graphs, involving topics such as clique decomposition, planarity, and automorphism groups. We also investigate and present a number of new results on orthogonal tree decompositions of complete graphs.
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Cairncross, Emily. "Proper 3-colorings of cycles and hypercubes." Oberlin College Honors Theses / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1621606265779497.

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Wong, Wiseley. "Spanning trees, toughness, and eigenvalues of regular graphs." Thesis, University of Delaware, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3595000.

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Spectral graph theory is a branch of graph theory which finds relationships between structural properties of graphs and eigenvalues of matrices corresponding to graphs. In this thesis, I obtain sufficient eigenvalue conditions for the existence of edge-disjoint spanning trees in regular graphs, and I show this is best possible. The vertex toughness of a graph is defined as the minimum value of [special characters omitted], where S runs through all subsets of vertices that disconnect the graph, and c(G\S ) denotes the number of components after deleting S. I obtain sufficient eigenvalue conditions for a regular graph to have toughness at least 1, and I show this is best possible. Furthermore, I determine the toughness value for many families of graphs, and I classify the subsets S of each family for when this value is obtained.

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King, Andrew James Howell. "On decomposition of complete infinite graphs into spanning trees." Thesis, University of Reading, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.253454.

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Zhang, Yuanping. "Counting the number of spanning trees in some special graphs /." View Abstract or Full-Text, 2002. http://library.ust.hk/cgi/db/thesis.pl?COMP%202002%20ZHANG.

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Koo, Cheng Wai. "A Bound on the Number of Spanning Trees in Bipartite Graphs." Scholarship @ Claremont, 2016. https://scholarship.claremont.edu/hmc_theses/73.

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Richard Ehrenborg conjectured that in a bipartite graph G with parts X and Y, the number of spanning trees is at most the product of the vertex degrees divided by |X|⋅|Y|. We make two main contributions. First, using techniques from spectral graph theory, we show that the conjecture holds for sufficiently dense graphs containing a cut vertex of degree 2. Second, using electrical network analysis, we show that the conjecture holds under the operation of removing an edge whose endpoints have sufficiently large degrees. Our other results are combinatorial proofs that the conjecture holds for graphs having |X| ≤ 2, for even cycles, and under the operation of connecting two graphs by a new edge. We also make two new conjectures based on empirical data, each of which is stronger than Ehrenborg's conjecture.
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Books on the topic "Spanning graphs of hypercubes"

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Deza. Scale-isometric polytopal graphs in hypercubes and cubic lattices: Polytopes in hypercubes and Zn̳. London: Imperial College Press, 2004.

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Grishukhin, Viacheslav, Mikhail I. Shtogrin, and Michel-Marie Deza. Scale-Isometric Polytopal Graphs in Hypercubes and Cubic Lattices: Polytopes in Hypercubes and Zn. Imperial College Press, 2004.

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Spanning Tree Results for Graphs and Multigraphs: A Matrix-Theoretic Approach. World Scientific Publishing Co Pte Ltd, 2014.

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Book chapters on the topic "Spanning graphs of hypercubes"

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Jungnickel, Dieter. "Spanning Trees." In Graphs, Networks and Algorithms, 99–127. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03822-2_4.

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Jungnickel, Dieter. "Spanning Trees." In Graphs, Networks and Algorithms, 103–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-32278-5_4.

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Ho, Ching-Tien. "Spanning Trees and Communication Primitives on Hypercubes." In Parallel Computing on Distributed Memory Multiprocessors, 47–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-58066-6_3.

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Akitaya, Hugo A., Maarten Löffler, and Csaba D. Tóth. "Multi-colored Spanning Graphs." In Lecture Notes in Computer Science, 81–93. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-50106-2_7.

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Deza, Michel Marie, and Monique Laurent. "Isometric Embeddings of Graphs into Hypercubes." In Algorithms and Combinatorics, 283–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-04295-9_19.

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Inoue, Keisuke, and Takao Nishizeki. "Spanning Distribution Forests of Graphs." In Frontiers in Algorithmics, 117–27. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08016-1_11.

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Kawabata, Masaki, and Takao Nishizeki. "Spanning Distribution Trees of Graphs." In Frontiers in Algorithmics and Algorithmic Aspects in Information and Management, 153–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38756-2_17.

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Baumslag, M., M. C. Heydemann, J. Opatrny, and D. Sotteau. "Embeddings of shuffle-like graphs in hypercubes." In Parle ’91 Parallel Architectures and Languages Europe, 179–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-662-25209-3_13.

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Kano, Mikio, Tomoki Yamashita, and Zheng Yan. "Spanning Caterpillars Having at Most k Leaves." In Computational Geometry and Graphs, 95–100. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-45281-9_9.

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Heun, Volker, and Ernst W. Mayr. "Embedding graphs with bounded treewidth into optimal hypercubes." In STACS 96, 155–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-60922-9_14.

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Conference papers on the topic "Spanning graphs of hypercubes"

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Qian, Yu, Baolei Cheng, Jianxi Fan, Yifeng Wang, and Ruofan Jiang. "Edge-disjoint spanning trees in the line graph of hypercubes." In 2021 IEEE 32nd International Conference on Application-specific Systems, Architectures and Processors (ASAP). IEEE, 2021. http://dx.doi.org/10.1109/asap52443.2021.00017.

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Yang, Jinn-Shyong, Jou-Ming Chang, and Hung–Chang Chan. "Independent Spanning Trees on Folded Hypercubes." In 2009 10th International Symposium on Pervasive Systems, Algorithms, and Networks. IEEE, 2009. http://dx.doi.org/10.1109/i-span.2009.55.

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Al-Tawil, Khalid, and Dimiter Avresky. "Reconfiguration of Spanning Trees in Faulty Hypercubes." In 1994 International Conference on Parallel Processing (ICPP'94). IEEE, 1994. http://dx.doi.org/10.1109/icpp.1994.173.

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Jiang, Qiang-rong, and Yuan Gao. "Spanning-Tree Kernels on Graphs." In 2010 International Conference on Measuring Technology and Mechatronics Automation (ICMTMA 2010). IEEE, 2010. http://dx.doi.org/10.1109/icmtma.2010.69.

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Liu, Yi-Jiun, Well Y. Chou, James K. Lan, and Chiuyuan Chen. "Constructing Independent Spanning Trees for Hypercubes and Locally Twisted Cubes." In 2009 10th International Symposium on Pervasive Systems, Algorithms, and Networks. IEEE, 2009. http://dx.doi.org/10.1109/i-span.2009.97.

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Day, Khaled, and Anand Tripathi. "Embedding Grids, Hypercubes, and Trees in Arrangement Graphs." In 1993 International Conference on Parallel Processing - ICPP'93 Vol3. IEEE, 1993. http://dx.doi.org/10.1109/icpp.1993.76.

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Azevedo, Marcelo Moraes de, Shahram Latifi, and Nader Bagherzadeh. "On Packing and Embedding Hypercubes into Star Graphs." In Simpósio de Arquitetura de Computadores e Processamento de Alto Desempenho. Sociedade Brasileira de Computação, 1994. http://dx.doi.org/10.5753/sbac-pad.1994.21873.

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Packing is a graph simulation technique hy which pk node-disjoint copies of a guest graph G(k) are embedded into a host graph H(n). Many advantages result from this technique as opposed to a simple embedding of G(k) into H(n). The multiple copies of G(k) can execute different instances of any algorithm designed to run in G(k), providing high throughput via an efficient, low-expansion utilization of H(n). Task migration mechanisms between the multiple copies of G(k) also become possible, allowing a proper allocation of the processors of H(n), load balancing and support of fault tolerance. Other advantages that arise from a well-devised packing technique are variable-dilation embeddings and multiple-sized packings. A variable-dilation embedding consists of connecting c copies of a graph G(k), packed into a host graph H(n) wilh dilation d, such as to obtain an emhedding of a graph G(k+l), l > 0, into H(n). The resulting embedding has dilation d when the nodes of G(k+l) communicate over the first k dimensions of G(k+l), and dilation di > d when a dimension i, k < i ≤ k + l, is used. Since many parallel algorithms use a restricted number of dimensions of the guest graph at any given step (e.g., SIMD-based algorithms), the resulting communication slowdown can be made significantly small on the average. We also extend the concept of connecting node-disjoint copies of a graph G(k) to obtain multiple-sized packings, in which graphs G(k), G(k + 1), ... , G(k + l) of various sizes are packed into a host graph H(n). Multiple-sized packings allow tasks with different processor requirements to be allocated proper guest graphs G(k + j) in H(n) (variable-dilation embeddings result when j > 0). This paper focuses on the problem of packing hypercubes Q(n-2) and Q(n-1) into a star graph S(n) with dilation 3. We show that 3 · [n/2]! · [(n-1)/2]! copies of Q(n-2) or [n/2]! · [(n-1)/2]! copies of Q(n-1) can be packed into S(n), with expansion n!/3 · [n/2]! · ((n-1)/2]! · 2n-2 and n!/ [n/2]! · [(n-1)/2]! · 2n-1, respectively. We also show how to connect packed Q(n-1)'s to obtain a variable-dilation embedding of Q(n - 1 + l), l ≤ [log2(ln/2]! · [(n-1)/2]!)], into S(n). Such an emhedding has dilation 3 for the first (n-1) dimensions of Q(n - 1 + l) and guarantees a minimal slowdown by using a slightly higher dilation (4 in most cases) for the remaining dimensions of Q(n - 1 + l). Finally, we also address the issue of multiple-sized packings of hypercubes into S(n).
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Svonava, Daniel, and Michail Vlachos. "Visualizing Graphs Using Minimum Spanning Dendrograms." In 2010 IEEE 10th International Conference on Data Mining (ICDM). IEEE, 2010. http://dx.doi.org/10.1109/icdm.2010.71.

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Rahmani, Mohammad Sohel, and Md Abul Kashem. "Degree restricted spanning trees of graphs." In the 2004 ACM symposium. New York, New York, USA: ACM Press, 2004. http://dx.doi.org/10.1145/967900.967949.

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Huang, Silu, Ada Wai-Chee Fu, and Ruifeng Liu. "Minimum Spanning Trees in Temporal Graphs." In SIGMOD/PODS'15: International Conference on Management of Data. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2723372.2723717.

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Reports on the topic "Spanning graphs of hypercubes"

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Mahoney, James. Tree Graphs and Orthogonal Spanning Tree Decompositions. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.2939.

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