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# Cheolwon Heo (허철원), The complexity of the matroid-homomorphism problems

## Monday, May 2, 2022 @ 4:30 PM - 5:30 PM KST

Room B332,
IBS (기초과학연구원)

In this talk, we introduce homomorphisms between binary matroids that generalize graph homomorphisms. For a binary matroid $N$, we prove a complexity dichotomy for the problem $\rm{Hom}_\mathbb{M}(N)$ of deciding if a binary matroid $M$ admits a homomorphism to $N$. The problem is polynomial-time solvable if $N$ has a loop or has no circuits of odd length, and is otherwise $\rm{NP}$-complete. We also get dichotomies for the list, extension, and retraction versions of the problem.

This is joint work with Hyobin Kim and Mark Siggers at Kyungpook National University.