Mathematics > Combinatorics
[Submitted on 8 Apr 2024 (v1), last revised 1 May 2024 (this version, v3)]
Title:On the chromatic number of powers of subdivisions of graphs
View PDFAbstract:For a given graph $G=(V,E)$, we define its \emph{$n$th subdivision} as the graph obtained from $G$ by replacing every edge by a path of length $n$. We also define the \emph{$m$th power} of $G$ as the graph on vertex set $V$ where we connect every pair of vertices at distance at most $m$ in $G$. In this paper we study the chromatic number of powers of subdivisions of graphs and resolve the case $m=n$ asymptotically. In particular, our result confirms a conjecture of Mozafari-Nia and Iradmusa in the case $m=n=3$ in a strong sense.
Submission history
From: Juanjo Rué Perna [view email][v1] Mon, 8 Apr 2024 14:09:52 UTC (31 KB)
[v2] Mon, 29 Apr 2024 15:22:15 UTC (28 KB)
[v3] Wed, 1 May 2024 10:11:58 UTC (28 KB)
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