无爪图及其扩展图的因子的研究

项目名称： 无爪图及其扩展图的因子的研究

项目编号： No.11426125

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 陈晓东

作者单位： 辽宁工业大学

项目金额： 3万元

中文摘要： 本项目分别构造Z闭包，N闭包，证明其能保证无爪图偶因子的存在性，并改进无爪图已有的圈闭包，边闭包，*-闭包使其同样保证无爪图偶因子的存在性;然后分别利用上述闭包研究无爪图的偶因子的分支数，周长，各分支所含任意最大独立集顶点数，并分别利用上述闭包及直接构造路因子的方法研究无爪图含有某些特殊路因子的充分条件；还证明对一般图均适用的邻域等价闭包能保证无爪图的扩展图（半无爪图，拟无爪图）的偶因子的存在性，并利用邻域等价闭包研究无爪图的扩展图的偶因子的分支数，周长，以及各因子分支含任意最大独立集顶点数；然后再分别利用邻域等价闭包，直接构造路因子的方法给出无爪图的扩展图含某些特殊路因子的充分条件。目前无爪图及其扩展图的研究结果大多是关于特殊的因子—连通的2-因子的性质，即Hamilton性质，本项目主要研究无爪图及其扩展图的较为一般的因子的性质，丰富了无爪图及其扩展图的研究理论。

中文关键词： 闭包；因子；无爪图；几乎无爪图；半无爪图

英文摘要： In this project, first we construct Z closure and N closure respectively, and prove that the two constructed closures can protect the existence of even factors of claw-free graphs and we improve the existed closures of claw-free graphs, which contain cycle closure, edge closure and *-closure, to make them also protect the existence of even factors of claw-free graphs. Then we mainly study the number and circumference of components, and the number of vertices of any maximum independent set in each component of even factors of claw-free graphs, and by the above closures and path factor construction, study the sufficient conditions, which make claw-free graphs contain some special path factors. Secondly, we prove that the neighborhood equivalence closure for general graphs can protect the existence of even factors of the generalizations of claw-free graphs (quasi-claw-free graphs and almost claw-free graphs), then we use the closure to study the number and circumference of components, and the number of vertices of any maximum independent set in each component of even factors of generalizations of claw-free graphs. Finally, we use the neighborhood equivalence closure and path factor construction to study the sufficient conditions, which make claw-free graphs contain some special path factors. At present, most of the

英文关键词： clousre；factor；claw-free graphs；almost claw-free graphs；quasi-claw-free graphs