Defective DP-colorings of sparse multigraphs

Jing, Yifan; Kostochka, Alexandr; Ma, Fuhong; Sittitrai, Pongpat; Xu, Jingwei

doi:10.48550/arxiv.1912.03421

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E(h T ) Is a Partition Of E(g)1

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2020

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Cited by 2 publications

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“…By definition, f DP (i, j, n) ≤ g DP (i, j, n). Recently [18], linear lower bounds on f DP (i, j, n) were proved that are exact for infinitely many n for every choice of i ≤ j.…”

Section: |E(g )|mentioning

confidence: 99%

Defective DP-colorings of sparse simple graphs

Jing¹,

Kostochka²,

Ma³

et al. 2020

Preprint

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DP-coloring (also known as correspondence coloring) is a generalization of list coloring developed recently by Dvořák and Postle. We introduce and study (i, j)-defective DP-colorings of simple graphs. Let g DP (i, j, n) be the minimum number of edges in an n-vertex DP-(i, j)-critical graph. In this paper we determine sharp bound on g DP (i, j, n) for each i ≥ 3 and j ≥ 2i + 1 for infinitely many n.

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“…By definition, f DP (i, j, n) ≤ g DP (i, j, n). Recently [18], linear lower bounds on f DP (i, j, n) were proved that are exact for infinitely many n for every choice of i ≤ j.…”

Section: |E(g )|mentioning

confidence: 99%

Defective DP-colorings of sparse simple graphs

Jing¹,

Kostochka²,

Ma³

et al. 2020

Preprint

Self Cite

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“…A graph G is h-defective k-choosable if for any k-list assignment L of G, there is an Lcolouring of G in which each vertex v has at most h-neighbours coloured the same colour as v. The concept of h-defective k-paintable is an online version of h-defective k-choosable, defined through a two-person game (see [7] for its definition), and h-defective k-DP-colourable is a generalization of h-defective k-choosable (see [9] for its definition). We remark that (d, h)decomposable graphs are easily seen to be h-defective (d + 1)-choosable, h-defective (d + 1)paintable, as well as h-defective (d+1)-DP-colourable.…”

Section: E(h T ) Is a Partition Of E(g)mentioning

confidence: 99%

Decomposing planar graphs into graphs with degree restrictions

Cho¹,

Choi²,

Kim³

et al. 2020

Preprint

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Given a graph G, a decomposition of G is a partition of its edges. A graph is (d, h)decomposable if its edge set can be partitioned into a d-degenerate graph and a graph with maximum degree at most h. For d ≤ 4, we are interested in the minimum integer h d such that every planar graph is (d, h d )-decomposable. It was known that h 3 ≤ 4 and h 2 ≤ 8 and h 1 = ∞. This paper proves that h 4 = 1, h 3 = 2 and 4 ≤ h 2 ≤ 6.

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Defective DP-colorings of sparse multigraphs

Cited by 2 publications

References 25 publications

Defective DP-colorings of sparse simple graphs

Defective DP-colorings of sparse simple graphs

Decomposing planar graphs into graphs with degree restrictions

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