Minimal bricks with the maximum number of edges

被引：0

作者：

Feng, Xing ^{[1
]}

Yan, Weigen ^{[1
]}

机构：

[1] School of Science, Jimei University, Xiamen, China

来源：

Journal of Graph Theory | 2025年 / 109卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Graph theory;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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 (Formula presented.), deleting (Formula presented.) results in a graph that is not a brick. Norine and Thomas proved that every minimal brick with (Formula presented.) vertices, which is distinct from the prism or the wheel on four, six, or eight vertices, has at most (Formula presented.) edges. In this paper, we characterize the extremal minimal bricks with (Formula presented.) vertices that meet this upper bound, and we prove that the number of extremal graphs equals (Formula presented.) if (Formula presented.), 5 if (Formula presented.), 10 if (Formula presented.) and 0 if (Formula presented.), respectively. © 2023 Wiley Periodicals LLC.

引用

页码：152 / 169