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arXiv · 2109.13887

Maximum diameter of $3$- and $4$-colorable graphs

Éva Czabarka·Stephen J. Smith·László Székely
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Abstract

P. Erdős, J. Pach, R. Pollack, and Z. Tuza [J. Combin. Theory, B 47 (1989), 279--285] made conjectures for the maximum diameter of connected graphs without a complete subgraph $K_{k+1}$, which have order $n$ and minimum degree $δ$. Settling a weaker version of a problem, by strengthening the $K_{k+1}$-free condition to $k$-colorable, we solve the problem for $k=3$ and $k=4$ using a unified linear programming duality approach. The case $k=4$ is a substantial simplification of the result of É. Czabarka, P. Dankelmann, and L. A. Székely [Europ. J. Comb., 30 (2009), 1082--1089].

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Éva Czabarka, Stephen J. Smith, László Székely. 2021-09-28. Maximum diameter of $3$- and $4$-colorable graphs. https://arxiv.org/abs/2109.13887

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