Proper interval vertex colorings of graphs

Tomáš Madaras, Daniela Matisová, Alfréd Onderko and Zuzana Šárošiová

Applied Mathematics and Computation, 2024, vol. 477, issue C

Abstract: In this paper, we explore proper vertex colorings of graphs with the additional constraint that the colors used on the closed neighborhood of every vertex form an integer interval; such colorings are called proper closed interval vertex colorings (PCIV colorings for short). As not every graph admits such a coloring, we are concerned with the problem of deciding which graphs admit PCIV colorings, describing several sufficient conditions (among them unique and 3-colorability, partial decomposability into two bipartite graphs, and density constraints) as well as some constructions of PCIV uncolorable graphs. We also present an algorithmic support for PCIV colorability based on a modification of the standard greedy algorithm for standard proper coloring.

Keywords: Proper coloring; Interval vertex coloring; Greedy coloring (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:477:y:2024:i:c:s0096300324002741

DOI: 10.1016/j.amc.2024.128813

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