The complexity of the matroid homomorphism problem
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Australian National University
2023
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| Online Access: | View Fulltext in Publisher View in Scopus |
| Summary: | 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. © 2023, Australian National University. All rights reserved. |
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| ISBN: | 10778926 (ISSN) |
| DOI: | 10.37236/11119 |