A vertex cover with chorded 4-cycles

作者:Gao, Yun Shu*; Li, Guo Jun; Yan, Jin
来源:Acta Mathematica Sinica-English Series, 2011, 27(12): 2351-2360.
DOI:10.1007/s10114-011-9531-y

摘要

Let k be an integer with k a parts per thousand yen 2 and G a graph with order n > 4k. We prove that if the minimum degree sum of any two nonadjacent vertices is at least n + k, then G contains a vertex cover with exactly k components such that k-1 of them are chorded 4-cycles. The degree condition is sharp in general.

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