摘要
Let k be an integer with k ≥ 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.
Let k be an integer with k ≥ 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.
基金
Supported by Natural Science Foundation of China （Grant Nos. 11161035, 10801091）, Research Crants from Ningxia University （Grant No. （E）ndzr09-1） and Scientific Research Project in Xinjiang （Grant No. XJEDU2009S101）
