A Vertex Cover with Chorded 4-cycles  

作　　者：Yun Shu GAO Guo Jun LI Jin YAN 

机构地区：[1]School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, P. R. China [2]Department of Biochemistry and Molecular Biology, University of Georgia, GA 30602, U.S.A. [3]School of Mathematics, Shandong University, Ji＇nan 250100, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第12期2351-2360,共10页数学学报（英文版）

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）

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.

关 键 词：Degree condition vertex-disjoint chorded quadrilateral 

分 类 号：O314[理学—一般力学与力学基础] TP301.6[理学—力学]