Planar graphs without specific cycles are 2-degenerate

Jumnongnit, Patcharapan; Pimpasalee, Wannapol

doi:10.1016/j.disc.2021.112488

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2023

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Cited by 4 publications

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“…Corollary 1.8 (Jumnongnit and Pimpasalee [4]). Every planar graph without 4-, 6-, 8-, and 10-cycles is 2-degenerate.…”

Section: Introductionmentioning

confidence: 97%

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Weak degeneracy of planar graphs without 4- and 6-cycles

Wang

2023

Preprint

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A graph is k-degenerate if every subgraph H has a vertex v with d H (v) ≤ k. The class of degenerate graphs plays an important role in the graph coloring theory. Observed that every k-degenerate graph is (k + 1)-choosable and (k + 1)-DP-colorable. Bernshteyn and Lee defined a generalization of k-degenerate graphs, which is called weakly k-degenerate. The weak degeneracy plus one is an upper bound for many graph coloring parameters, such as choice number, DP-chromatic number and DP-paint number. In this paper, we give two sufficient conditions for a plane graph without 4-and 6-cycles to be weakly 2-degenerate, which implies that every such graph is 3-DP-colorable and near-bipartite, where a graph is near-bipartite if its vertex set can be partitioned into an independent set and an acyclic set.

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“…Corollary 1.8 (Jumnongnit and Pimpasalee [4]). Every planar graph without 4-, 6-, 8-, and 10-cycles is 2-degenerate.…”

Section: Introductionmentioning

confidence: 97%

“…* Center for Applied Mathematics, Henan University, Kaifeng, 475004, China. Email: wangtao@henu.edu.cn Jumnongnit and Pimpasalee [4] gave some sufficient conditions for planar graphs without 4and 6-cycles to be 2-degenerate.…”

Section: Introductionmentioning

confidence: 99%