On (2,r)-choosability of planar graphs without short cycles

Jianfeng Hou and Hongguo Zhu

Applied Mathematics and Computation, 2023, vol. 444, issue C

Abstract: For a graph G and two positive integers t,r, a (t,t+r)-list assignment of G is a function L that assigns a set of permissible colors L(u) to every vertex u such that |L(u)|≥t and |L(u)∪L(w)|≥t+r when uw is an edge. The graph G is said to be (t,t+r)-choosable if G allows a proper coloring ψ satisfying ψ(u)∈L(u) for each u∈V(G) and each (t,t+r)-list assignment L of G. In this paper, we consider the (2,2+r)-choosability of planar graphs without short cycles. We show that: (1) if G is a planar graph contains no cycles of length 4, then G is (2,9)-choosable; (2) if G is a planar graph contains no cycles of lengths 4 and 5, then G is (2,7)-choosable.

Keywords: Choosability; Planar graphs; Ck-free; Discharging (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:444:y:2023:i:c:s0096300322008980

DOI: 10.1016/j.amc.2022.127830

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