2 -turán's Theorem
نویسنده
چکیده
In the following material, we use the notion of an independent set of a graph G: this is a set of I vertices of G such that no two vertices of I are adjacent in G. These are sometimes referred to as stable sets in the literature. The chromatic number of a graph G, denoted χ(G), is the smallest r such that V (G) has a partition into independent sets V1, V2, . . . , Vr. In other words, we may assign r colors to the vertices of G in such a way that no two vertices of the same color r adjacent. Such graphs are also called r-partite. The graph G is a complete r-partite graph if all edges between Vi and Vj are present for i, j : 1 ≤ i < j ≤ r. We say G is a balanced r-partite graph if |V1| ≤ |V2| ≤ · · · ≤ |Vr| ≤ |V1|+ 1.
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