与不相交匹配对有关的饱和图的特征

IF 0.6 Q3 MATHEMATICS

Illinois Journal of Mathematics Pub Date : 2020-11-23 DOI:10.1215/00192082-9719963

Zhengda Mo, Sam Qunell, A. Tserunyan, Jenna Zomback

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引用次数: 0

摘要

我们研究了在有限图中具有最大总边数的任意对不相交匹配中最大匹配的大小与最大可能匹配的大小之比。之前已经证明这个比值在4/5和1之间，并且该类图达到4/5是完全表征的。在本文中，我们首先证明了图分解为路径和甚至循环为研究这个比值提供了一种新的方法。然后，我们使用这种技术来描述在所有图中达到比率1的图，这些图可以通过选择最大匹配和最大不相交匹配来覆盖。

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Characterization of saturated graphs related to pairs of disjoint matchings

We study the ratio, in a finite graph, of the sizes of the largest matching in any pair of disjoint matchings with the maximum total number of edges and the largest possible matching. Previously, it was shown that this ratio is between 4/5 and 1, and the class of graphs achieving 4/5 was completely characterized. In this paper, we first show that graph decompositions into paths and even cycles provide a new way to study this ratio. We then use this technique to characterize the graphs achieving ratio 1 among all graphs that can be covered by a certain choice of a maximum matching and maximum disjoint matchings.

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来源期刊

Illinois Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： IJM strives to publish high quality research papers in all areas of mainstream mathematics that are of interest to a substantial number of its readers. IJM is published by Duke University Press on behalf of the Department of Mathematics at the University of Illinois at Urbana-Champaign.