Elsevier

Discrete Applied Mathematics

Volume 185, 20 April 2015, Pages 1-7
Discrete Applied Mathematics

Exact value of ex(n;{C3,,Cs}) for n25(s1)8

https://doi.org/10.1016/j.dam.2014.11.021Get rights and content
Under an Elsevier user license
open archive

Abstract

For integers s8 and s+1n25(s1)8, we determine the exact value of the function ex(n;{C3,,Cs}), that represents the maximum number of edges in a {C3,,Cs}-free graph of order n. This result was already known when 3s7. To do that, for 1k5, we provide a family of graphs  Hsk such that e(Hsk)n(Hsk)=k and with the property that Hsk reaches girth  s+1 with the minimum number of vertices. Also, we determine an infinity family of solutions of the problem ex(n;{C3,,Cs})=n+6.

Keywords

Extremal function
Extremal graphs
Forbidden cycles
Girth

Cited by (0)