## Algebra and Combinatorics Seminar

**Date: ** February 2, 2024

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 302

**Speaker: **Youngho Yoo, TAMU

**Title: ***Minimum degree conditions for apex-outerplanar minors*

**Abstract: **Motivated by Hadwiger's conjecture, we study graphs H for which every graph with minimum degree at least |V(H)|-1 contains H as a minor. We prove that a large class of apex-outerplanar graphs satisfies this property. Our result gives the first examples of such graphs whose vertex cover numbers are significantly larger than a half of its vertices, and recovers all known such graphs that have arbitrarily large maximum degree. Our proof can be adapted to directed graphs to show that every directed graph with minimum out-degree at least t contains a certain orientation of the wheel and of every apex-tree on t+1 vertices as a subdivision and a butterfly minor respectively. Joint work with Chun-Hung Liu.