Choosability with union separation of planar graphs without intersecting triangles

Xinhong Pang and Min Chen

Applied Mathematics and Computation, 2025, vol. 502, issue C

Abstract: Let G be a graph, and let k,s be two positive integers. A k-list assignment of G is called a (k,k+s)-list assignment if, for any two adjacent vertices u and v, |L(u)∪L(v)|≥k+s. A graph G is said to be (k,k+s)-choosable if, for every given (k,k+s)-list assignment, it always admits a proper coloring π such that π(v)∈L(v) for every v∈V(G). In this paper, we demonstrate that every planar graph without intersecting triangles is (3,7)-choosable. This strengthens a result which asserts that every triangle-free planar graph is (3,7)-choosable.

Keywords: Choosability with union separation; Planar graph; (k,k + s)-choosable; Intersecting triangles (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:502:y:2025:i:c:s009630032500219x

DOI: 10.1016/j.amc.2025.129493

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