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Structure in sparse kk-critical graphs

By Ron Gould and others
Recently, Kostochka and Yancey proved that a conjecture of Ore is asymptotically true by showing that every kk-critical graph satisfies E(G)(k21k1)V(G)k(k3)2(k1).|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 kk-Ore graphs. We show that for any k33k\geq33... Show more
July 2, 2021
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Structure in sparse $k$-critical graphs
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