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Extremal graphs for odd wheels
【Abstract】 For a graph H , the Turán number of H , denoted by ex ( n , H ) , is the maximum number of edges of an n -vertex H -free graph. Let g ( n , H ) denote the maximum number of edges not contained in any monochromatic copy of H in a 2-edge-coloring of K n . A wheel W m is a graph formed by connecting a single vertex to all vertices of a cycle of length m − 1 . The Turán number of W 2 k was determined by Simonovits in 1960s. In this paper, we determine ex ( n , W 2 k + 1 ) when n is sufficiently large. We also show that, for sufficient large n , g ( n , W 2 k + 1 ) = ex ( n , W 2 k + 1 ) which confirms a conjecture posed by Keevash and Sudakov for odd wheels.
【Author】 Long-Tu Yuan
【Keywords】 decomposition family, Turán number, wheels
【Journal】 Journal of Graph Theory(IF：1) Time：2021-08-04