Relevant bibliographies by topics / 2-connected outerplanar graphs

Academic literature on the topic '2-connected outerplanar graphs'

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Published: 25 May 2024

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Journal articles on the topic "2-connected outerplanar graphs"

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DRMOTA, MICHAEL, OMER GIMÉNEZ, and MARC NOY. "The Maximum Degree of Series-Parallel Graphs." Combinatorics, Probability and Computing 20, no. 4 (May 31, 2011): 529–70. http://dx.doi.org/10.1017/s0963548311000198.

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We prove that the maximum degree Δn of a random series-parallel graph with n vertices satisfies Δn/logn → c in probability, and Δn ~ c logn for a computable constant c > 0. The same kind of result holds for 2-connected series-parallel graphs, for outerplanar graphs, and for 2-connected outerplanar graphs.
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Velona, Vasiliki. "Encoding and avoiding 2-connected patterns in polygon dissections and outerplanar graphs." Discrete Mathematics 341, no. 12 (December 2018): 3402–14. http://dx.doi.org/10.1016/j.disc.2018.08.027.

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Tang, Yunfeng, Huixin Yin, and Miaomiao Han. "Star edge coloring of $ K_{2, t} $-free planar graphs." AIMS Mathematics 8, no. 6 (2023): 13154–61. http://dx.doi.org/10.3934/math.2023664.

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<abstract><p>The star chromatic index of a graph $ G $, denoted by $ \chi{'}_{st}(G) $, is the smallest number of colors required to properly color $ E(G) $ such that every connected bicolored subgraph is a path with no more than three edges. A graph is $ K_{2, t} $-free if it contains no $ K_{2, t} $ as a subgraph. This paper proves that every $ K_{2, t} $-free planar graph $ G $ satisfies $ \chi_{st}'(G)\le 1.5\Delta +20t+20 $, which is sharp up to the constant term. In particular, our result provides a common generalization of previous results on star edge coloring of outerplanar graphs by Bezegová et al.(2016) and of $ C_4 $-free planar graphs by Wang et al.(2018), as those graphs are subclasses of $ K_{2, 3} $-free planar graphs.</p></abstract>
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Brezovnik, Simon, Niko Tratnik, and Petra Žigert Pleteršek. "Resonance Graphs and a Binary Coding of Perfect Matchings of Outerplane Bipartite Graphs." Match Communications in Mathematical and in Computer Chemistry 90, no. 2 (April 2023): 453–68. http://dx.doi.org/10.46793/match.90-2.453b.

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The aim of this paper is to investigate resonance graphs of 2- connected outerplane bipartite graphs, which include various families of molecular graphs. Firstly, we present an algorithm for a binary coding of perfect matchings of these graphs. Further, 2- connected outerplane bipartite graphs with isomorphic resonance graphs are considered. In particular, it is shown that if two 2- connected outerplane bipartite graphs are evenly homeomorphic, then its resonance graphs are isomorphic. Moreover, we prove that for any 2-connected outerplane bipartite graph G there exists a catacondensed even ring systems H such that the resonance graphs of G and H are isomorphic. We conclude with the characterization of 2-connected outerplane bipartite graphs whose resonance graphs are daisy cubes.
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Leydold, Josef, and Peter F. Stadler. "Minimal Cycle Bases of Outerplanar Graphs." Electronic Journal of Combinatorics 5, no. 1 (February 27, 1998). http://dx.doi.org/10.37236/1354.

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Chan, Tsz Lung. "Contractible Edges in 2-Connected Locally Finite Graphs." Electronic Journal of Combinatorics 22, no. 2 (June 15, 2015). http://dx.doi.org/10.37236/4414.

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In this paper, we prove that every contraction-critical 2-connected infinite graph has no vertex of finite degree and contains uncountably many ends. Then, by investigating the distribution of contractible edges in a 2-connected locally finite infinite graph $G$, we show that the closure of the subgraph induced by all the contractible edges in the Freudenthal compactification of $G$ is 2-arc-connected. Finally, we characterize all 2-connected locally finite outerplanar graphs nonisomorphic to $K_3$ as precisely those graphs such that every vertex is incident to exactly two contractible edges as well as those graphs such that every finite bond contains exactly two contractible edges.
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Kraus, Veronika. "The degree distribution in unlabelled $2$-connected graph families." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AM,..., Proceedings (January 1, 2010). http://dx.doi.org/10.46298/dmtcs.2773.

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International audience We study the random variable $X_n^k$, counting the number of vertices of degree $k$ in a randomly chosen $2$-connected graph of given families. We prove a central limit theorem for $X_n^k$ with expected value $\mathbb{E}X_n^k \sim \mu_kn$ and variance $\mathbb{V}X_n^k \sim \sigma_k^2n$, both asymptotically linear in $n$, for both rooted and unrooted unlabelled $2$-connected outerplanar or series-parallel graphs.
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Feng, Xinge, Xingchao Deng, and Junqing Cai. "Anti-van der Waerden Numbers of Some 2-Connected Outerplanar Graphs." Journal of Interconnection Networks, April 6, 2024. http://dx.doi.org/10.1142/s0219265924500051.

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Given a graph [Formula: see text] and a positive integer [Formula: see text], the anti-van der Waerden number [Formula: see text] is defined as the minimum positive integer [Formula: see text] such that every exact [Formula: see text]-coloring of the vertices of [Formula: see text] admits a rainbow [Formula: see text]-AP. In this paper, we determine the exact value of [Formula: see text] if [Formula: see text] is a [Formula: see text]-connected outerplanar graph with diameters [Formula: see text].
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Liu, Qi, and Douglas B. West. "Tree-Thickness and Caterpillar-Thickness under Girth Constraints." Electronic Journal of Combinatorics 15, no. 1 (July 21, 2008). http://dx.doi.org/10.37236/817.

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We study extremal problems for decomposing a connected $n$-vertex graph $G$ into trees or into caterpillars. The least size of such a decomposition is the tree thickness $\theta_{\bf T}(G)$ or caterpillar thickness $\theta_{\bf C}(G)$. If $G$ has girth $g$ with $g\ge 5$, then $\theta_{\bf T}(G)\le \lfloor{n/g}\rfloor+1$. We conjecture that the bound holds also for $g=4$ and prove it when $G$ contains no subdivision of $K_{2,3}$ with girth 4. For $\theta_{\bf C}$, we prove that $\theta_{\bf C}(G)\le\lceil{(n-2)/4}\rceil$ when $G$ has girth at least $6$ and is not a $6$-cycle. For triangle-free graphs, we conjecture that $\theta_{\bf C}(G)\le\lceil{3n/8}\rceil$ and prove it for outerplanar graphs. For $2$-connected graphs with girth $g$, we conjecture that $\theta_{\bf C}(G)\le \lfloor{n/g}\rfloor$ when $n\ge\max\{6,g^2/2\}$ and prove it for outerplanar graphs. All the bounds are sharp (sharpness in the $\lceil{3n/8}\rceil$ bound is shown only for $n\equiv 5$ mod $8$).
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Davis, Robert, and Tianran Chen. "Computing Volumes of Adjacency Polytopes via Draconian Sequences." Electronic Journal of Combinatorics 29, no. 1 (March 25, 2022). http://dx.doi.org/10.37236/9768.

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Adjacency polytopes appear naturally in the study of nonlinear emergent phenomena in complex networks. The ``"PQ-type" adjacency polytope, denoted $\nabla^{\mathrm{PQ}}_G$ and which is the focus of this work, encodes rich combinatorial information about power-flow solutions in sparse power networks that are studied in electric engineering. Of particular importance is the normalized volume of such an adjacency polytope, which provides an upper bound on the number of distinct power-flow solutions. In this article we show that the problem of computing normalized volumes for $\nabla^{\mathrm{PQ}}_G$ can be rephrased as counting $D(G)$-draconian sequences where $D(G)$ is a certain bipartite graph associated to the network. We prove recurrences for all networks with connectivity at most $1$ and, for $2$-connected graphs under certain restrictions, we give recurrences for subdividing an edge and taking the join of an edge with a new vertex. Together, these recurrences imply a simple, non-recursive formula for the normalized volume of $\nabla^{\mathrm{PQ}}_G$ when $G$ is part of a large class of outerplanar graphs; we conjecture that the formula holds for all outerplanar graphs. Explicit formulas for several other (non-outerplanar) classes are given. Further, we identify several important classes of graphs $G$ which are planar but not outerplanar that are worth additional study.
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Dissertations / Theses on the topic "2-connected outerplanar graphs"

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Dai, Tianjiao. "Some vertex colouring problems and a generalisation of Hamilton-connectivity in graphs." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG067.

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La décomposition des graphes fait référence au processus de décomposer un graphe complexe en composantes plus simples et plus petites, souvent dans le but d'analyser ou de résoudre des problèmes liés au graphe. Il s'agit d'un outil important pour représenter la structure globale et les propriétés d'une manière plus détaillée. Il est aussi également utile pour résoudre des problèmes impliquant la recherche de structures spécifiques dans un graphe. Il existe plusieurs types courants de techniques de décomposition de graphe largement utilisées en théorie des graphes et dans des domaines connexes, notamment la décomposition en arbres, la décomposition en blocs, la décomposition modulaire, la décomposition hiérarchique, etc. Cette thèse étudie deux types de décomposition de sommets d'un graphe : les colorations propres (décomposition en ensembles indépendants) et la Hamilton-connectivité (décomposition en chemins internement disjoints entre deux ensembles où les chemins couvrent tous les sommets du graphe)
The decomposition of graphs refers to the process of breaking down a complex graph into simpler, smaller components, often with the goal of analysing or solving problems related to the graph. It is an important tool to display the global structure and properties in a more fine-grained manner, and also useful in solving problems that involve finding specific structures in a graph. There are several common types of graph decomposition techniques that are widely used in graph theory and related fields, including tree decomposition, block decomposition, modular decomposition, hierarchical decomposition, etc. This thesis studies two kinds of vertex decomposition of a graph: proper colourings (decomposition into independent sets) and Hamilton-connectivity (decomposition into internally-disjoint paths between two sets where the paths cover all the vertices of graphs)
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Book chapters on the topic "2-connected outerplanar graphs"

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Read, Ronald C., and Robin J. Wilson. "Planar Graphs." In An Atlas Of Graphs, 229–62. Oxford University PressOxford, 1998. http://dx.doi.org/10.1093/oso/9780198532897.003.0005.

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Abstract A graph G is planar if it can be drawn in the plane or on the surface of a sphere so that no two edges meet, except at a vertex at which both are incident. Such a drawing partitions the set of points of the plane or sphere not lying on G into faces; for example, the following drawing has 6 faces. A graph G is outerplanar if G can be drawn in the plane so that all the vertices lie on the boundary of the exterior face. Euler’s formula states that, if a connected planar graph G has n vertices and e edges, then any drawing of G in the plane or on the sphere has/ faces, where n −e +f = 2.
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Journal articles
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