Deletable edges in 3-connected graphs and their applications

Abstract: I will analyze 3-connected graphs that contain a fixed 3-connected graph $H$ as a minor, but in which no edge can be deleted while preserving 3-connectivity and an $H$-minor. Let $G$ and $H$ be simple 3-connected graph such that $G$ has an $H$-minor.  An edge $e$ in $G$ is called $H$-deletable if $G\backslash e$ is 3-connected and has an $H$-minor. If $G$ has no $H$-deletable edge, then $G$ can be reduced to $H$ using three specific local operations.  This gives a framework for studying extremal graphs with no $H$-deletable edges and yields applications to excluded-minor questions. This talk is based on a paper in Discrete Mathematics (Vol 349, Issue 6).

number theory

Audience: researchers in the topic

Combinatorial and additive number theory seminar (CANT 2026)