Exact generalized Turán number for K3 versus suspension of P4

Abstract

Let P4 denote the path graph on 4 vertices. The suspension of P4, denoted by Pˆ4, is the graph obtained via adding an extra vertex and joining it to all four vertices of P4. In this note, we demonstrate that for n≥8, the maximum number of triangles in any n-vertex graph not containing Pˆ4 is ⌊n2/8⌋. Our method uses simple induction along with computer programming to prove a base case of the induction hypothesis.