2022/09/22 by Jingru Yan, Yan, Jingru
Computer Science · Mathematics · #05C35 #05C38 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2209.10828
openalex publication_date 2022/09/22 · openalex created_date 2022/09/25 · openalex updated_date 2026/07/28
Given a graph H and a positive integer n, the Turán number of H for the order n, denoted ex(n,H), is the maximum size of a simple graph of order n not containing H as a subgraph. Given graphs G and H, the notation G \vee H means the joint of G and H. χ(G) denotes the chromatic number of a graph G. Since χ(Km \vee C2k-1)=m+3 and there is an edge e∈ E(Km \vee C2k-1) such that χ(Km \vee C2k-1-e)= m+2, by the Simonovits theorem, ex(n, Km \vee C2k-1) = \lfloor ((m+1)n2)/(2(m+2))\rfloor for sufficiently large n. In this paper, we prove that 2(m+2)k-3(m+2)-1 is large enough for n.