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arXiv · 1911.00109

Regular Turán numbers

Yair Caro·Zsolt Tuza
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Abstract

The regular Turán number of a graph $F$, denoted by rex$(n,F)$, is the largest number of edges in a regular graph $G$ of order $n$ such that $G$ does not contain subgraphs isomorphic to $F$. Giving a partial answer to a recent problem raised by Gerbner et al. [arXiv:1909.04980] we prove that rex$(n,F)$ asymptotically equals the (classical) Turán number whenever the chromatic number of $F$ is at least four; but it is substantially different for some 3-chromatic graphs $F$ if $n$ is odd.

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Yair Caro, Zsolt Tuza. 2019-10-31. Regular Turán numbers. https://arxiv.org/abs/1911.00109

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