April 11, 2024

Graphs with girth 9 and without longer odd holes are 3‐colourable

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Resumen

Abstract For a number , let denote the family of graphs which have girth and have no odd hole with length greater than . Wu, Xu and Xu conjectured that every graph in is 3‐colourable. Chudnovsky et al., Wu et al., and Chen showed that every graph in , and is 3‐colourable, respectively. In this paper, we prove that every graph in is 3‐colourable. This confirms Wu, Xu and Xu's conjecture.

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Cite This Study

Wang et al. (Thu,) studied this question.

synapsesocial.com/papers/68e6f858b6db64358767306b https://doi.org/https://doi.org/10.1002/jgt.23101

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4On a Conjecture Concerning the Petersen Graph: Part II2014 · 11 citations
5Bisimplicial vertices in even-hole-free graphs2008 · 65 citations

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