By Ron Gould and others

Recently, Kostochka and Yancey proved that a conjecture of Ore is asymptotically true by showing that every $k$-critical graph satisfies $|E(G)|\geq\left\lceil\left(\frac{k}{2}-\frac{1}{k-1}\right)|V(G)|-\frac{k(k-3)}{2(k-1)}\right\rceil.$ They also characterized the class of graphs that attain this bound and showed that it is equivalent to the set of $k$-Ore graphs. We show that for any $k\geq33$... Show more

July 2, 2021

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Structure in sparse $k$-critical graphs

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