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...
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| Format: | Article |
| Language: | English |
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Australian National University
2023
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| Online Access: | View Fulltext in Publisher View in Scopus |
| LEADER | 01298nam a2200169Ia 4500 | ||
|---|---|---|---|
| 001 | 10.37236-11119 | ||
| 008 | 230529s2023 CNT 000 0 und d | ||
| 020 | |a 10778926 (ISSN) | ||
| 245 | 1 | 0 | |a The complexity of the matroid homomorphism problem |
| 260 | 0 | |b Australian National University |c 2023 | |
| 856 | |z View Fulltext in Publisher |u https://doi.org/10.37236/11119 | ||
| 856 | |z View in Scopus |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-85159725408&doi=10.37236%2f11119&partnerID=40&md5=98abc52d0b3c8906cb3f6abb3f5de917 | ||
| 520 | 3 | |a 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. | |
| 700 | 1 | 0 | |a Heo, C. |e author |
| 700 | 1 | 0 | |a Kim, H. |e author |
| 700 | 1 | 0 | |a Siggers, M. |e author |
| 773 | |t Electronic Journal of Combinatorics | ||