The Turán Number of The Graph 3P5

Abstract

The Turán number ex(n, H) of a graph H, is the maximum number of edges in a graph of order n which does not contain H as a subgraph. Let Pi denote a path consisting of i vertices and let mPi denote m disjoint copies of Pi. In this paper we give the Turán number ex(n, 3P5) for all positive integers n, which partly solve the conjecture proposed by Long-Tu Yuan and Xiao-Dong Zhang [7]. Moreover, we characterize all extremal graphs of 3P5 denote by Ex(n, 3P5).