961
个编辑
更改
跳到导航
跳到搜索
第49行：
第49行： − + 第57行：
第57行： − 一个图的无弦环（也可以称为孔或诱导环），指的是该环中没有两个顶点通过不属于该环的边相连。其反孔部分为此图孔的补图。无弦环可用于表征完美图：通过强完美图定理，当且仅当它的孔或反孔部分中无奇数（且大于3）个顶点时，图才是完美的。弦图是完美图的特殊形式，即没有任何长度大于三的孔。+ 第65行：
第65行： − 图的围长是其最小环的长度；并且这个环必须是无弦的。笼定义为具有给定度和围长组合的最小正则图。+ 第73行：
第73行： − 一个图中的边环具有以下性质：不在此边环上的两条连边可以通过一条特殊路径连接，该路径内部顶点均不在此边环上。如果一个图中的某条环并非通过加一条边形成，那么其边环肯定是诱导环。+
→Chordless cycles 无弦环
== Chordless cycles 无弦环 ==
== Chordless cycles 无弦环 ==
[[文件:Graph with Chordless and Chorded Cycles.svg.png|200px|thumb|left|此图中的绿色环（A-B-C-D-E-F-A）是无弦的，而红色环（G-H-I-J-K-L-G）则是有弦的。因为连边K-I是弦。]]
[[文件:Graph with Chordless and Chorded Cycles.svg.png|200px|thumb|right|此图中的绿色环（A-B-C-D-E-F-A）是无弦的，而红色环（G-H-I-J-K-L-G）则是有弦的。因为连边K-I是弦。]]
A chordless cycle in a graph, also called a hole or an induced cycle, is a cycle such that no two vertices of the cycle are connected by an edge that does not itself belong to the cycle. An antihole is the complement of a graph hole. Chordless cycles may be used to characterize perfect graphs: by the strong perfect graph theorem, a graph is perfect if and only if none of its holes or antiholes have an odd number of vertices that is greater than three. A chordal graph, a special type of perfect graph, has no holes of any size greater than three.
A chordless cycle in a graph, also called a hole or an induced cycle, is a cycle such that no two vertices of the cycle are connected by an edge that does not itself belong to the cycle. An antihole is the complement of a graph hole. Chordless cycles may be used to characterize perfect graphs: by the strong perfect graph theorem, a graph is perfect if and only if none of its holes or antiholes have an odd number of vertices that is greater than three. A chordal graph, a special type of perfect graph, has no holes of any size greater than three.
一个图的无弦环Chordless cycles（也可以称为孔Hole或导出环Induced cycle），指的是该环中没有两个顶点通过不属于该环的边相连。其反孔部分为此图孔的补图。无弦环i可用于表征完美图Perfect graphs：通过强完美图定理，当且仅当它的孔或反孔部分中无奇数（且大于3）个顶点时，图才是完美的。弦图是完美图的特殊形式，即没有任何长度大于三的孔。
The girth of a graph is the length of its shortest cycle; this cycle is necessarily chordless. Cages are defined as the smallest regular graphs with given combinations of degree and girth.
The girth of a graph is the length of its shortest cycle; this cycle is necessarily chordless. Cages are defined as the smallest regular graphs with given combinations of degree and girth.
图的围长Girth是其最小环的长度；并且这个环必须是无弦的。笼Cages定义为具有给定度和围长组合的最小正则图。
A peripheral cycle is a cycle in a graph with the property that every two edges not on the cycle can be connected by a path whose interior vertices avoid the cycle. In a graph that is not formed by adding one edge to a cycle, a peripheral cycle must be an induced cycle.
A peripheral cycle is a cycle in a graph with the property that every two edges not on the cycle can be connected by a path whose interior vertices avoid the cycle. In a graph that is not formed by adding one edge to a cycle, a peripheral cycle must be an induced cycle.
一个图中的边环Peripheral cycle具有以下性质：不在此边环上的两条连边可以通过一条特殊路径连接，该路径内部顶点均不在此边环上。如果一个图中的某条环并非通过加一条边形成，那么其边环肯定是导出环。
== Cycle space 环空间 ==
== Cycle space 环空间 ==