On Dynamic Coloring of Graphs
Meysam Alishahi

TL;DR
This paper investigates upper bounds on the dynamic chromatic number of graphs, especially regular graphs, and introduces bounds for the dynamic list chromatic number, advancing understanding of graph coloring constraints.
Contribution
It provides new upper bounds for the dynamic chromatic and list chromatic numbers of regular graphs, including a logarithmic bound related to degree.
Findings
Bound: (G) \u2212 (G) + c \u2212 1 for some constant c
Upper bounds for the dynamic list chromatic number of regular graphs
Establishment of a relationship between degree and dynamic coloring parameters
Abstract
A dynamic coloring of a graph is a proper coloring such that for every vertex of degree at least 2, the neighbors of receive at least 2 colors. In this paper we present some upper bounds for the dynamic chromatic number of graphs. In this regard, we shall show that there is a constant such that for every -regular graph , . Also, we introduce an upper bound for the dynamic list chromatic number of regular graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory
