On the chromatic number of powers of subdivisions of graphs

For a given graph G=(V,E), we define its nth subdivision as the graph obtained from G by replacing every edge by a path of length n. We also define the mth 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 chromati...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 360; pp. 506 - 511
Main Authors Anastos, Michael, Boyadzhiyska, Simona, Rathke, Silas, Rué, Juanjo
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.01.2025
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Summary:For a given graph G=(V,E), we define its nth subdivision as the graph obtained from G by replacing every edge by a path of length n. We also define the mth 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.
ISSN:0166-218X
DOI:10.1016/j.dam.2024.10.002