Extremal Triangle-Free Regular Graphs Containing A Cut Vertex

Abstract

The exact values of $c(n)$ are determined, where $c(n)$ denotes the largest $k$ for which there exists a triangle-free $k$-regular graph on $n$ vertices containing a cut-vertex. As a corollary, we obtain a lower bound on the densest triangle-free regular graphs of given order that do not have a one-factorization.