On the Halin Turán number of short cycles

Abstract

A Halin graph is a graph constructed by embedding a tree with no vertex of degree two in the plane and then adding a cycle to join the tree’s leaves. The Halin Turán number of a graph F , denoted as exH(n, F ), is the maximum number of edges in an n-vertex Halin graph. In this paper, we give the exact value of exH(n, C4), where C4 is a cycle of length 4. We also pose a conjecture for the Halin Turán number of longer cycles.