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Stability for Vertex Cycle Covers
2017
Electronic Journal of Combinatorics
In 1996 Kouider and Lonc proved the following natural generalization of Dirac's Theorem: for any integer $k\geq 2$, if $G$ is an $n$-vertex graph with minimum degree at least $n/k$, then there are $k-1$ cycles in $G$ that together cover all the vertices.This is tight in the sense that there are $n$-vertex graphs that have minimum degree $n/k-1$ and that do not contain $k-1$ cycles with this property. A concrete example is given by $I_{n,k} = K_n\setminus K_{(k-1)n/k+1}$ (an edge-maximal graph
doi:10.37236/5185
fatcat:segewcfzsbfdpajj4tnqqotdw4