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Characterization and chromatic number of triangle-free graphs with diameter 2

arXiv CS Wednesday 03 June 2026, 04:00 UTC By Akihiro Higashitani, Diogo Kendy Matsumoto, Naoki Matsumoto 1 min read
Key Points

arXiv:2606.03267v1 Announce Type: cross Abstract: In this paper, we consider triangle-free graphs with diameter 2. If a triangle-free graph $G$ with diameter 2 is not isomorphic to a star, then the radius of $G$ is also 2, where such a graph is also called a $2$-self-centered graph. [A characterization for 2-self-centered graphs, Discuss.

arXiv:2606.03267v1 Announce Type: cross Abstract: In this paper, we consider triangle-free graphs with diameter 2. If a triangle-free graph $G$ with diameter 2 is not isomorphic to a star, then the radius of $G$ is also 2, where such a graph is also called a $2$-self-centered graph. Shekarriz et al. [A characterization for 2-self-centered graphs, Discuss. Math. Graph Theory 38 (2018), 27--37.] gave a characterization of 2-self-centered graphs. However, there is a slight flaw in their characterization. Thus, in this paper, we modify it and prove an accurate characterization of those graphs. Furthermore, by using our characterization, we prove some results concerning the chromatic number of triangle-free graphs with diameter 2.
Shekarriz et al (PERSON)
Originally published by arXiv CS Read original →

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