具有最大边缘数量的最小砖块

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2023-08-16 DOI:10.1002/jgt.23026

Xing Feng, Weigen Yan

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引用次数: 0

摘要

如果在去除任何两个不同的顶点后，得到的图具有完美匹配，那么3连通图就是一块砖。如果对于每条边，删除会导致图形不是砖块，则砖块是最小的。Norine和Thomas证明了每一个有顶点的最小砖块，与四个、六个或八个顶点上的棱镜或轮子不同，都有最多的边。在本文中，我们刻画了顶点满足该上界的极值极小砖块，并证明了极值图的数量分别等于if、5 if、10 if和0 if。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Minimal bricks with the maximum number of edges

A 3‐connected graph is a brick if, after the removal of any two distinct vertices, the resulting graph has a perfect matching. A brick is minimal if, for every edge , deleting results in a graph that is not a brick. Norine and Thomas proved that every minimal brick with vertices, which is distinct from the prism or the wheel on four, six, or eight vertices, has at most edges. In this paper, we characterize the extremal minimal bricks with vertices that meet this upper bound, and we prove that the number of extremal graphs equals if , 5 if , 10 if and 0 if , respectively.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .