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Journal articles on the topic 'Fractional colourings'

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Author: Grafiati

Published: 25 May 2024

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1

Kilakos, K., and O. Marcotte. "Fractional and integral colourings." Mathematical Programming 76, no. 2 (February 1997): 333–47. http://dx.doi.org/10.1007/bf02614444.

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2

Zakharov, Pavel Aleksandrovich, and Dmitry Aleksandrovich Shabanov. "Fractional colourings of random hypergraphs." Russian Mathematical Surveys 78, no. 6 (2023): 1161–63. http://dx.doi.org/10.4213/rm10151e.

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3

Khennoufa, Riadh, and Olivier Togni. "Total and fractional total colourings of circulant graphs." Discrete Mathematics 308, no. 24 (December 2008): 6316–29. http://dx.doi.org/10.1016/j.disc.2007.11.070.

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4

Kaiser, Tomáš, Andrew King, and Daniel Králʼ. "Fractional total colourings of graphs of high girth." Journal of Combinatorial Theory, Series B 101, no. 6 (November 2011): 383–402. http://dx.doi.org/10.1016/j.jctb.2010.12.005.

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5

Ryan, Jennifer. "Fractional total colouring." Discrete Applied Mathematics 27, no. 3 (June 1990): 287–92. http://dx.doi.org/10.1016/0166-218x(90)90073-l.

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6

Meagher, Conor, and Bruce Reed. "Fractionally total colouring." Electronic Notes in Discrete Mathematics 19 (June 2005): 297–303. http://dx.doi.org/10.1016/j.endm.2005.05.040.

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7

Reed, Bruce, and Paul Seymour. "Fractional Colouring and Hadwiger's Conjecture." Journal of Combinatorial Theory, Series B 74, no. 2 (November 1998): 147–52. http://dx.doi.org/10.1006/jctb.1998.1835.

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8

Kilakos, K., and B. Reed. "Fractionally colouring total graphs." Combinatorica 13, no. 4 (December 1993): 435–40. http://dx.doi.org/10.1007/bf01303515.

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9

Davies, Ewan, Rémi Joannis de Verclos, Ross J. Kang, and François Pirot. "Occupancy fraction, fractional colouring, and triangle fraction." Journal of Graph Theory 97, no. 4 (March 9, 2021): 557–68. http://dx.doi.org/10.1002/jgt.22671.

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10

Meagher, Conor, and Bruce Reed. "Fractionally total colouring Gn,p." Discrete Applied Mathematics 156, no. 7 (April 2008): 1112–24. http://dx.doi.org/10.1016/j.dam.2007.05.052.

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11

Gdawiec, Krzysztof, Wiesław Kotarski, and Agnieszka Lisowska. "Visual Analysis of the Newton’s Method with Fractional Order Derivatives." Symmetry 11, no. 9 (September 9, 2019): 1143. http://dx.doi.org/10.3390/sym11091143.

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The aim of this paper is to investigate experimentally and to present visually the dynamics of the processes in which in the standard Newton’s root-finding method the classic derivative is replaced by the fractional Riemann–Liouville or Caputo derivatives. These processes applied to polynomials on the complex plane produce images showing basins of attractions for polynomial zeros or images representing the number of iterations required to obtain polynomial roots. These latter images were called by Kalantari as polynomiographs. We use both: the colouring by roots to present basins of attractions, and the colouring by iterations that reveal the speed of convergence and dynamic properties of processes visualised by polynomiographs.

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12

Hasemann, Henning, Juho Hirvonen, Joel Rybicki, and Jukka Suomela. "Deterministic local algorithms, unique identifiers, and fractional graph colouring." Theoretical Computer Science 610 (January 2016): 204–17. http://dx.doi.org/10.1016/j.tcs.2014.06.044.

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13

Kim, Se-Jin, IlKwon Cho, Chhorn Sok, and Sang-Hyun Bae. "Graph colouring based fractional frequency reuse for enterprise femtocell networks." IET Communications 11, no. 12 (August 24, 2017): 1831–37. http://dx.doi.org/10.1049/iet-com.2016.0891.

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14

Kennedy, W. Sean, Conor Meagher, and Bruce A. Reed. "Fractionally Edge Colouring Graphs with Large Maximum Degree in Linear Time." Electronic Notes in Discrete Mathematics 34 (August 2009): 47–51. http://dx.doi.org/10.1016/j.endm.2009.07.008.

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15

Norin, Sergey, Alex Scott, and David R. Wood. "Clustered colouring of graph classes with bounded treedepth or pathwidth." Combinatorics, Probability and Computing, July 5, 2022, 1–12. http://dx.doi.org/10.1017/s0963548322000165.

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Abstract The clustered chromatic number of a class of graphs is the minimum integer $k$ such that for some integer $c$ every graph in the class is $k$ -colourable with monochromatic components of size at most $c$ . We determine the clustered chromatic number of any minor-closed class with bounded treedepth, and prove a best possible upper bound on the clustered chromatic number of any minor-closed class with bounded pathwidth. As a consequence, we determine the fractional clustered chromatic number of every minor-closed class.

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16

Gutowski, Grzegorz. "Mr. Paint and Mrs. Correct go Fractional." Electronic Journal of Combinatorics 18, no. 1 (July 1, 2011). http://dx.doi.org/10.37236/627.

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We study a fractional counterpart of the on-line list colouring game "Mr. Paint and Mrs. Correct" introduced recently by Schauz. We answer positively a question of Zhu by proving that for any given graph the on-line choice ratio and the (off-line) choice ratio coincide. On the other hand it is known from the paper of Alon et al. that the choice ratio equals the fractional chromatic number. It was also shown that the limits used in the definitions of these last two notions can be realised. We show that this is not the case for the on-line choice ratio. Both our results are obtained by exploring the strong links between the on-line choice ratio, and a new on-line game with probabilistic flavour which we introduce.

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17

Li, Yaqi, Shuwei Zhai, Yani Liu, Jingwei Zhang, Ziyuan Meng, Jincheng Zhuang, Haifeng Feng, et al. "Electronic Flat Band in Distorted Colouring Triangle Lattice." Advanced Science, October 15, 2023. http://dx.doi.org/10.1002/advs.202303483.

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AbstractDispersionless flat bands (FBs) in momentum space, given rise to electron destructive interference in frustrated lattices, offer opportunities to enhance electronic correlations and host exotic many‐body phenomena, such as Wigner crystal, fractional quantum hall state, and superconductivity. Despite successes in theory, great challenges remain in experimentally realizing FBs in frustrated lattices due to thermodynamically structural instability. Here, the observation of electronic FB in a potassium distorted colouring triangle (DCT) lattice is reported, which is supported on a blue phosphorene‐gold network. It is verified that the interaction between potassium and the underlayer dominates and stabilizes the frustrated structures. Two‐dimensional electron gas is modulated by the DCT lattice, and in turn results in a FB dispersion due to destructive quantum interferences. The FB exhibits suppressed bandwidth with high density of states, which is directly observed by scanning tunneling microscopy and confirmed by the first‐principles calculation. This work demonstrates that DCT lattice is a promising platform to study FB physics and explore exotic phenomena of correlation and topological matters.

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