Exact results for generalized extremal problems forbidding an even cycle

2022/08/04 by Győri, Ervin, He, Zhen, Lv, Zequn +4
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.02538

Abstract

We determine the maximum number of copies of K_s,s in a C_2s+2-free n-vertex graph for all integers s ≥ 2 and sufficiently large n. Moreover, for s∈\2,3\ and any integer n we obtain the maximum number of cycles of length 2s in an n-vertex C_2s+2-free bipartite graph.

Related

• Many vertex-disjoint even cycles of fixed length in a graph
• Generalized Tur'an problems for even cycles
• The maximum number of copies of an even cycle in a planar graph
• Counting triangles in graphs without vertex disjoint odd cycles
• Maximising the number of induced cycles in a graph