关于图的最小等分

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-07-21 DOI:10.1002/jgt.23284

Jianfeng Hou, Shufei Wu

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引用次数: 0

摘要

图的等分是其顶点集的二分，其中两个部分的顶点数最多相差1，其大小是穿过这两个部分的边的数量。设G是一个有n个顶点和m条边的图。Bollobás和Scott问了下面的问题：用G的等分我们能保证的最大和最小的切点是什么？有合理的充分条件使G的等分大小至少为m / 2 + cN对于某个c >； 0。在本文中，我们研究了在许多情况下出现的最小对分问题，并初步给出G的等分大小不超过m / 2−c的充分条件N对于某个c >； 0。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On Min-Bisections of Graphs

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On Min-Bisections of Graphs

A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two parts differ by at most 1, and its size is the number of edges which go across the two parts. Let $G$ be a graph with $n$ vertices and $m$ edges. Bollobás and Scott asked the following: What are the largest and smallest cuts that we can guarantee with bisections of $G$ ? There are reasonable sufficient conditions such that $G$ has bisections of size at least $m / 2 + c n$ for some $c > 0$ . In this paper, we study the Min-Bisection problem which has arisen in numerous contexts, and initially give some sufficient conditions such that $G$ has bisections of size at most $m / 2 - c n$ for some $c > 0$ .

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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 .