﻿ 二部图中过特定点的点不交弦圈 Vertex-Disjoint Chorded Cycles through Specified Vertices in Bipartite Graphs

Vol.07 No.04(2018), Article ID:24677,5 pages
10.12677/AAM.2018.74051

Vertex-Disjoint Chorded Cycles through Specified Vertices in Bipartite Graphs

Xiaoyao Lin, Yunshu Gao

School of Mathematics and Statistics, Ningxia University, Yinchuan Ningxia

Received: Apr. 11th, 2018; accepted: Apr. 21st, 2018; published: Apr. 28th, 2018

ABSTRACT

A chord is an edge between two vertices of a cycle that is not an edge on the cycle. If a cycle has at least one chord, then the cycle is called a chorded cycle. The minimum degree condition is given for a bipartite graph to contain vertex-disjoint chorded cycles containing specified vertices.

Keywords:Vertex-Disjoint Chorded Cycles, Bipartite Graphs, Minimum Degree

1. 引言

1963年，Moon和Moser [3] 给出了二部图中存在哈密尔顿圈的Dirac型条件：

2. 定理1.5的证明

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，则由，可得

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。不失一般性，不妨设。令。首先考虑的情形。如果，那么是弦。如果，那么是弦。

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Vertex-Disjoint Chorded Cycles through Specified Vertices in Bipartite Graphs[J]. 应用数学进展, 2018, 07(04): 413-417. https://doi.org/10.12677/AAM.2018.74051

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