Choosability with union separation of planar graphs without cycles of length 4

Jianfeng Hou and Hongguo Zhu

Applied Mathematics and Computation, 2020, vol. 386, issue C

Abstract: For a graph G and a positive integer k, a k-list assignment of G is a function L on the vertices of G such that for each vertex v ∈ V(G), |L(v)| ≥ k. Let s be a nonnegative integer. Then L is a (k,k+s)-list assignment of G if |L(u)∪L(v)|≥k+s for each edge uv. If for each (k,k+s)-list assignment L of G, G admits a proper coloring φ such that φ(v) ∈ L(v) for each v ∈ V(G), then we say G is (k,k+s)-choosable. This refinement of choosability is called choosability with union separation by Kumbhat, Moss and Stolee, who showed that all planar graphs are (3, 11)-choosable. In this paper, we prove that every planar graph without cycles of length 4 is (3,6)-choosable.

Keywords: Choosability; Planar graph; C4-free; Discharge (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304367

DOI: 10.1016/j.amc.2020.125477

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