A Minimum Degree Result for Disjoint Cycles and Forests in Graphs

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on s edges and k disjoint cycles. The main result is the following theorem. Let F be a forest on s edges without isolated vertices and let G be a graph of order at least with minimum degree at least , where k, s are nonnegative integers. Then G contains the disjoint union of the forest F and k disjoint cycles. This theorem provides a common generalization of previous results of Corrádi & Hajnal [4] and Brandt [3] who considered the cases (cycles only) and (forests only), respectively.

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Received: October 13, 1995

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Schuster, G. A Minimum Degree Result for Disjoint Cycles and Forests in Graphs. Combinatorica 18, 425–436 (1998). https://doi.org/10.1007/PL00009831

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  • AMS Subject Classification (1991) Classes:  05C05, 05C35, 05C38