Turán’s graph theorem, measures and probability theory
نویسنده
چکیده
Let us start with the well-known graph theorem of Turán that determines the largest number of edges in a graph on n vertices containing no complete graph on k + 1 vertices. If 1 ≤ k ≤ n are integers, define the graph T (n, k) whose vertex set is V1 ∪ V2 ∪ . . . ∪ Vk where the Vis are pairwise disjoint and their sizes are either ⌊ n k ⌋ or ⌈ n k ⌉ and two vertices are adjacent if and only if they are in two different Vis. It is easy to see that T (n, k) contains no complete graph on k + 1 vertices. The number of edges of T (n, k) is denoted by t(n, k).
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تاریخ انتشار 2013