961
个编辑
更改
跳到导航
跳到搜索
第13行：
第13行： − In the [[mathematics|mathematical]] field of [[graph theory]], a '''bipartite graph''' (or '''bigraph''') is a [[Graph (discrete mathematics)|graph]] whose [[vertex (graph theory)|vertices]] can be divided into two [[disjoint sets|disjoint]] and [[Independent set (graph theory)|independent sets]] <math>U</math> and <math>V</math> such that every [[edge (graph theory)|edge]] connects a vertex in <math>U</math> to one in <math>V</math>. Vertex sets <math>U</math> and <math>V</math> are usually called the ''parts'' of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length [[cycle (graph theory)|cycles]].<ref name=diestel2005graph>{{cite book|last=Diestel|first=Reinard|title=Graph Theory, Grad. Texts in Math|year=2005|publisher=Springer|isbn=978-3-642-14278-9|url=http://diestel-graph-theory.com/}}</ref><ref>{{citation − + + + +
无编辑摘要
节点数分别为m=5和n=3的两个集合所组成的一个完整二分图
节点数分别为m=5和n=3的两个集合所组成的一个完整二分图
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets <math>U</math> and <math>V</math> such that every edge connects a vertex in <math>U</math> to one in <math>V</math>. Vertex sets <math>U</math> and <math>V</math> are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles.<ref>{{citation
In the [[mathematics|mathematical]] field of [[graph theory]], a '''bipartite graph''' (or '''bigraph''') is a [[Graph (discrete mathematics)|graph]] whose [[vertex (graph theory)|vertices]] can be divided into two [[disjoint sets|disjoint]] and [[Independent set (graph theory)|independent sets]] <math>U</math> and <math>V</math> such that every [[edge (graph theory)|edge]] connects a vertex in <math>U</math> to one in <math>V</math>. Vertex sets <math>U</math> and <math>V</math> are usually called the ''parts'' of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length [[cycle (graph theory)|cycles]].<ref name=diestel2005graph>{{cite book|last=Diestel|first=Reinard|title=Graph Theory, Grad. Texts in Math|year=2005|publisher=Springer|isbn=978-3-642-14278-9|url=http://diestel-graph-theory.com/}}</ref><ref>
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets {\displaystyle U}U and {\displaystyle V}V such that every edge connects a vertex in {\displaystyle U}U to one in {\displaystyle V}V. Vertex sets {\displaystyle U}U and {\displaystyle V}V are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles.[1][2]
在图论的数学领域中，二分图（或二部图）内的所有顶点可以分为两个不相交且独立的集合U和集合V，并且每个连边（无向或有向）的两个顶点分别在集合U和集合V当中。通常集合U和集合V被称为该二分图的子集。同时，二分图中不包含任何形式的奇数环，即：集合U和集合V构造的点集所形成的循环圈边数不为奇数。
在图论的数学领域中，二分图（或二部图）内的所有顶点可以分为两个不相交且独立的集合U和集合V，并且每个连边（无向或有向）的两个顶点分别在集合U和集合V当中。通常集合U和集合V被称为该二分图的子集。同时，二分图中不包含任何形式的奇数环，即：集合U和集合V构造的点集所形成的循环圈边数不为奇数。