Cycle Covering of Plane Triangulations

Abstract

Bondy conjectures that if $G$ is a $2$-edge-connected simple graph with $n$ vertices, then at most $(2n-1)/3$ cycles in $G$ will cover $G$. In this note, we show that if $G$ is a plane triangulation with $n\ge 6$ vertices, then at most $(2n-3)/3$ cycles in $G$ will cover $G$.