Turán Graph
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High Quality Content by WIKIPEDIA articles! The Turán graph T(n,r) is a graph formed by partitioning a set of n vertices into r subsets, with sizes as equal as possible, and connecting two vertices by an edge whenever they belong to different subsets. The graph will have (nmod r) subsets of size lceil n/rrceil, and r (nmod r) subsets of size lfloor n/rrfloor. That is, it is a complete r-partite graph K_{lceil n/rrceil, lceil n/rrceil, ldots, lfloor n/rrfloor, lfloor n/rrfloor}. Each vertex has degree either n-lceil n/rrceil or n-lfloor n/rrfloor. The number of edges is at most…mehr

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High Quality Content by WIKIPEDIA articles! The Turán graph T(n,r) is a graph formed by partitioning a set of n vertices into r subsets, with sizes as equal as possible, and connecting two vertices by an edge whenever they belong to different subsets. The graph will have (nmod r) subsets of size lceil n/rrceil, and r (nmod r) subsets of size lfloor n/rrfloor. That is, it is a complete r-partite graph K_{lceil n/rrceil, lceil n/rrceil, ldots, lfloor n/rrfloor, lfloor n/rrfloor}. Each vertex has degree either n-lceil n/rrceil or n-lfloor n/rrfloor. The number of edges is at most left(1-frac1rright)frac{n^2}{2}. It is a regular graph, if n is divisible by r.