Extremal graphs for odd wheels

Abstract

Abstract For a graph , the Turán number of , denoted by ex, is the maximum number of edges of an ‐vertex ‐free graph. Let denote the maximum number of edges not contained in any monochromatic copy of in a 2‐edge‐coloring of . A wheel is a graph formed by connecting a single vertex to all vertices of a cycle of length . The Turán number of was determined by Simonovits in 1960s. In this paper, we determine ex when is sufficiently large. We also show that, for sufficient large , which confirms a conjecture posed by Keevash and Sudakov for odd wheels.