Extremal $K_4$-minor-free graphs without short cycles

Abstract

We determine the maximum number of edges in a $K_4$-minor-free $n$-vertex graph of girth $g$, when $g=5$ or $g$ is even. We argue that there are many different $n$-vertex extremal graphs, if $n$ is even and $g$ is odd.

arXiv commentto appear in Periodica Mathematica Hungarica