On list 3-dynamic coloring of near-triangulations
Ruijuan Gu, Seog-Jin Kim, Yulai Ma, Yongtang Shi

TL;DR
This paper investigates list 3-dynamic coloring of near-triangulation planar graphs, establishing an improved upper bound of 6 for the list 3-dynamic chromatic number, which is tighter than the general bound for all planar graphs.
Contribution
It proves that near-triangulation planar graphs have a list 3-dynamic chromatic number at most 6, improving bounds for this specific class.
Findings
ch_3^d(G) 6 for near-triangulations
Better upper bounds than general planar graphs
Enhanced understanding of dynamic coloring in specific planar graph classes
Abstract
An -dynamic -coloring of a graph is a proper -coloring such that for any vertex , there are at least distinct colors in . The -dynamic chromatic number of a graph is the least such that there exists an -dynamic -coloring of . The list -dynamic chromatic number of a graph is denoted by . Loeb et al. showed that for every planar graph , and there is a planar graph with . In this paper, we study a special class of planar graphs which have better upper bounds of . We prove that if is a planar graph which is near-triangulation, where a near-triangulation is a planar graph whose bounded faces are all 3-cycles.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory
