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单词 KneserGraphs
释义

Kneser graphs


Let k,n be positive integers with kn. The Kneser graphMathworldPlanetmath Kn:k has as its vertex set the (nk) k-element subsets of {1,2,,n}. Two vertices are adjacent if and only if they correspond to disjoint subsets.

The graph Kn:1 is the complete graphMathworldPlanetmath on n vertices. Another well-known Kneser graph is K5:2, better known as the Petersen graphMathworldPlanetmath, which is shown in figure 1. The Petersen graph is often a counterexample to graph-theoretical conjectures.

Figure 1: The Petersen graph
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更新时间:2025/5/4 9:02:25