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On Degree Sum Conditions and Vertex-Disjoint Chorded Cycles (1911.08686v1)
Published 20 Nov 2019 in math.CO
Abstract: In this paper, we consider a general degree sum condition sufficient to imply the existence of $k$ vertex-disjoint chorded cycles in a graph $G$. Let $\sigma_t(G)$ be the minimum degree sum of $t$ independent vertices of $G$. We prove that if $G$ is a graph of sufficiently large order and $\sigma_t(G)\geq 3kt-t+1$ with $k\geq 1$, then $G$ contains $k$ vertex-disjoint chorded cycles. We also show that the degree sum condition on $\sigma_t(G)$ is sharp. To do this, we also investigate graphs without chorded cycles.