Online coloring graphs with high girth and high oddgirth
Judit Nagy-Gyorgy
TL;DR
This paper establishes upper bounds on the online chromatic number for graphs with high girth and oddgirth, extending Kierstead's algorithm to broader classes of graphs without small cycles.
Contribution
It generalizes Kierstead's algorithm to graphs with high girth and oddgirth, providing new upper bounds for their online chromatic number.
Findings
Upper bounds for online chromatic number of high girth graphs
Extension of Kierstead's algorithm to graphs with high oddgirth
Generalization to graphs excluding small cycles
Abstract
We give an upper bound for the online chromatic number of graphs with high girth and for graphs with high oddgirth generalizing Kier- stead's algorithm for graphs that contain neither a C3 or C5 as an induced subgraph.
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Taxonomy
TopicsOptimization and Search Problems · Graph Labeling and Dimension Problems · Advanced Graph Theory Research