On chromatic numbers of some distance graphs
D. Zakharov
TL;DR
This paper investigates the chromatic numbers of specific distance graphs, providing exact values for infinitely many cases and improving bounds in many other scenarios.
Contribution
It determines the chromatic numbers of $G(n,3,2)$ for infinitely many n and enhances upper bounds for $ ext{chi}(G(n,r,s))$ in numerous cases.
Findings
Exact chromatic numbers for $G(n,3,2)$ in infinitely many cases
Improved upper bounds for $ ext{chi}(G(n,r,s))$ in many scenarios
Enhanced understanding of coloring properties of distance graphs
Abstract
In this paper we find chromatic numbers of distance graphs for infinitely many n. Also we improve upper bound for in large part of cases.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph Labeling and Dimension Problems · Advanced Graph Theory Research