On list r-hued coloring of outer-1-planar graphs

Lingmei Liang, Fengxia Liu and Hong-Jian Lai

Applied Mathematics and Computation, 2023, vol. 440, issue C

Abstract: Let L be list assignment of colors available for vertices of a graph G, an (L,r)-coloring of G is a proper coloring c such that for any vertex v∈V(G), we have c(v)∈L(v) and |c(N(v))|≥min{d(v),r}. The r-hued list chromatic number of G, denoted as χL,r(G), is the least integer k, such that for list assignment L satisfying |L(v)|=k∀v∈V(G), G has an (L,r)-coloring. A graph G is an outer-1-planar graph if G has a drawing on the plane such that all vertices of V(G) are located on the outer face of this drawing, and each edge can cross at most one other edge. For any positive integer r, we completely determine the upper bound of list r-hued chromatic number for all outer-1-planar graphs. This extended a former result in [Discrete Mathematics and Theoretical Computer Science, 23:3 (2021)].

Keywords: Outer-1-planar graphs; (L,r)-coloring; List r-hued chromatic number (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007299

DOI: 10.1016/j.amc.2022.127658

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