Abstract
We show that for every binary matroid N there is a graph D(N) such that for the graphic matroid M(G) of a graph G, there is a matroid homomorphism from M(G) to N if and only if there is a graph homomorphism from G to D(N). With this we prove a complexity dichotomy for the problem HomM(N) of deciding if a binary matroid M admits a matroid homomorphism to N. The problem is polynomial time solvable if N has a loop or has no circuits of odd length, and is otherwise NP-complete. We also get dichotomies for the list, extension, and retraction versions of the problem.
Original language | English |
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Article number | P2.27 |
Journal | Electronic Journal of Combinatorics |
Volume | 30 |
Issue number | 2 |
DOIs | |
State | Published - 2023 |