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完全二分图.
完全二分图 |
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一个完全二分图m=3 n =2 |
顶点 | n+m |
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边 | mn |
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自同构群 | 2m!n!如果m=n,否则m!n! |
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完全二分图是一种特殊的二分图,可以把图中的顶点分成两个集合,使得第一个集合中的所有顶点都与第二个集合中的所有顶点相连。
完全二分图是一个二分图,使得对于任何两个顶点和,都是中的一条边。且的完全二分图记为。
- 平面图不能含有子图;外平面图不能含有子图(这些是必要条件而不是充分条件)。
- 完全二分图的顶点覆盖数为,边覆盖数为。
- 完全二分图具有大小为的最大独立集。
- 完全二分图具有大小为的最大匹配。
- 完全二分图具有正则的n-边染色。
- 完全二分图有mn-1 nm-1个不同的生成树。
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