A note on the number of triangles in graphs without the suspension of a path on four vertices

2022/03/23 by Gerbner, Dániel · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.12527

Abstract

The suspension of the path P₄ consists of a P₄ and an additional vertex connected to each of the four vertices, and is denoted by P₄. The largest number of triangles in a P₄-free n-vertex graph is denoted by ex(n,K₃,P₄). Mubayi and Mukherjee in 2020 showed that ex(n,K₃,P₄)= n²/8+O(n). We show that for sufficiently large n, ex(n,K₃,P₄)=\lfloor n²/8\rfloor.

Cited by

• The generalized Turán number for K₃ in graphs without suspensions of a path on five vertices

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