请输入您要查询的字词:

 

单词 BipartiteGraph
释义

bipartite graph


A bipartite graphMathworldPlanetmath is a graph with a chromatic numberMathworldPlanetmath of 2.

The following graph, for example, is bipartite:

\\xymatrixA\\ar@-[rrr]\\ar@-[rd]\\ar@-[ddd]&&&B&E&F\\ar@-[ur]\\ar@-[l]\\ar@-[d]&&H\\ar@-[u]\\ar@-[r]\\ar@-[dl]&G&D&&&C\\ar@-[uuu]\\ar@-[lll]\\ar@-[ul]

One way to think of a bipartite graph is by partitioning the vertices into two disjoint sets where vertices in one set are adjacent only to vertices in the other set. In the above graph, this may be more obvious with a different :

\\xymatrixA\\ar@-[r]\\ar@-[rd]\\ar@-[rdd]&EF\\ar@-[ru]\\ar@-[r]\\ar@-[rdd]&BH\\ar@-[ruu]\\ar@-[r]\\ar@-[rd]&DC\\ar@-[ruu]\\ar@-[ru]\\ar@-[r]&G

The two subsets are the two columns of vertices, all of which have the same colour.

A graph is bipartite if and only if all its cycles have even length. This is easy to see intuitively: any path of odd length on a bipartite must end on a vertex of the opposite colour from the beginning vertex and hence cannot be a cycle.

随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 10:58:04