Homomorphisms of planar signed graphs to signed projective cubes
We conjecture that every signed graph of unbalanced girth 2g, whose underlying graph is bipartite and planar, admits a homomorphism to the signed projective cube of dimension 2g1. Our main result is to show that for a given g, this conjecture is equivalent to the corresponding case (k = 2g) of a con...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2013-09-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/612/pdf |
| _version_ | 1827323787695095808 |
|---|---|
| author | Reza Naserasr Edita Rollova Eric Sopena |
| author_facet | Reza Naserasr Edita Rollova Eric Sopena |
| author_sort | Reza Naserasr |
| collection | DOAJ |
| description | We conjecture that every signed graph of unbalanced girth 2g, whose underlying graph is bipartite and planar, admits a homomorphism to the signed projective cube of dimension 2g1. Our main result is to show that for a given g, this conjecture is equivalent to the corresponding case (k = 2g) of a conjecture of Seymour claiming that every planar k-regular multigraph with no odd edge-cut of less than k edges is k-edge-colorable. To this end, we exhibit several properties of signed projective cubes and establish a folding lemma for planar even signed graphs. |
| first_indexed | 2024-04-25T01:58:08Z |
| format | Article |
| id | doaj.art-0ecc3da774d24e53b45d5db7406071e7 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:58:08Z |
| publishDate | 2013-09-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-0ecc3da774d24e53b45d5db7406071e72024-03-07T15:27:44ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502013-09-01Vol. 15 no. 310.46298/dmtcs.612612Homomorphisms of planar signed graphs to signed projective cubesReza NaserasrEdita Rollovahttps://orcid.org/0000-0003-1508-932XEric SopenaWe conjecture that every signed graph of unbalanced girth 2g, whose underlying graph is bipartite and planar, admits a homomorphism to the signed projective cube of dimension 2g1. Our main result is to show that for a given g, this conjecture is equivalent to the corresponding case (k = 2g) of a conjecture of Seymour claiming that every planar k-regular multigraph with no odd edge-cut of less than k edges is k-edge-colorable. To this end, we exhibit several properties of signed projective cubes and establish a folding lemma for planar even signed graphs.https://dmtcs.episciences.org/612/pdfhomomorphismplanar signed graphprojective cubesigned graph[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Reza Naserasr Edita Rollova Eric Sopena Homomorphisms of planar signed graphs to signed projective cubes Discrete Mathematics & Theoretical Computer Science homomorphism planar signed graph projective cube signed graph [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Homomorphisms of planar signed graphs to signed projective cubes |
| title_full | Homomorphisms of planar signed graphs to signed projective cubes |
| title_fullStr | Homomorphisms of planar signed graphs to signed projective cubes |
| title_full_unstemmed | Homomorphisms of planar signed graphs to signed projective cubes |
| title_short | Homomorphisms of planar signed graphs to signed projective cubes |
| title_sort | homomorphisms of planar signed graphs to signed projective cubes |
| topic | homomorphism planar signed graph projective cube signed graph [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/612/pdf |
| work_keys_str_mv | AT rezanaserasr homomorphismsofplanarsignedgraphstosignedprojectivecubes AT editarollova homomorphismsofplanarsignedgraphstosignedprojectivecubes AT ericsopena homomorphismsofplanarsignedgraphstosignedprojectivecubes |