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Cut-edges and Regular Subgraphs in Odd-degree Regular Graphs

Douglas B. West 教授(美国University of Illinois)
Friday, April 12th, 2019, 3:00 PM  闵行数学楼401报告厅
报告人简介:Douglas West教授是杰出的图论学家,在图论的很多领域都做出了有价值的贡献。他也十分重视整理和传播图论知识,例如他写的《图论导引》是一本很好的教材和参考书。目前他还在写几本组合数学方面的专著。West教授的成就和贡献受到了同行的广泛尊敬,他现在是著名专业杂志Discrete Mathematics 的主编。

报告内容简介:An l-factor in a graph is a subgraph containing every vertex, such that every vertex has degree l. Hanson, Loten, and Toft proved that every (2r+1)-regular graph with at most 2r cut-edges has a 2-factor. We generalize this: For k <= (2r+1)/3, every (2r+1)-regular graph with at most 2r-3(k-1) cut-edges has a 2k-factor. The restrictions on k and on the number of cut-edges are sharp. We characterize the graphs with exactly 2r-3(k-1)+1 cut-edges but no 2k-factor. For k>(2r+1)/3, there are graphs without cut-edges that have no 2k-factor.
(Joint work with Alexandr V. Kostochka, Andr\'e Raspaud, Bjarne Toft, and Dara Zirlin.)

主持人:詹兴致 教授
主办单位:数学科学学院 科技处
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