%0 Journal Article
%T 一些图的弱外部平衡划分<br>Weak External Bisection of Some Graphs
%A 刘玉敏
%J Pure Mathematics
%P 520-526
%@ 2160-7605
%D 2024
%I Hans Publishing
%R 10.12677/PM.2024.142050
%X 设G是一个图。G的一个2-划分是V(G)的一个2-划分，即V(G)=V<sub>1</sub>∪V<sub>2</sub>且V<sub>1</sub>∩V<sub>2</sub>= ？。如果一个2-划分满足||V<sub>1</sub>|-|V<sub>2</sub>||≤1，我们就称其为平衡划分。本文的研究主要基于Bollobás和Scott提出的一个猜想：每个图G都有一个平衡划分(V<sub>1</sub>,V<sub>2</sub>)，对于V<sub>1</sub>中的每一个顶点v，v的邻点中至少有一半减去一个在V<sub>2</sub>中；对于V<sub>2</sub>中的每一个顶点v，v的邻点中至少有一半减去一个在V<sub>1</sub>中。在本文中，将对二部图、皇冠图以及风车图证实这一猜想。<br />
Let G be a graph. A bipartition of G is a bipartition of V(G) with V(G)=V<sub>1</sub>∪V<sub>2</sub> and V<sub>1</sub>∩V<sub>2</sub>= ？. If a bipartition satisfies ||V<sub>1</sub>|-|V<sub>2</sub>||≤1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott: every graph G has a bisection (V<sub>1</sub>,V<sub>2</sub>) such that ？v∈V<sub>1</sub>, at least half minus one of the neighbors of v are in the V<sub>2</sub>;？v∈V<sub>2</sub>, at least half minus one of the neighbors of v are in the V1. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.
%K 弱外部平衡划分，二部图，皇冠图，风车图<br>Weak External Bisection
%K Bipartite Graph
%K Crown Graph
%K Windmill Graph
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=81412