On Nowhere Zero 4-Flows in Regular Matroids
Walton and Welsh proved that if a co-loopless regular matroid M does not have a minor in {M(K(3,3)),M∗(K5)}, then M admits a nowhere zero 4-flow. Lai, Li and Poon proved that if M does not have a minor in {M(K5),M∗(K5)}, then M admits a nowhere zero 4-flow. We prove that if a co-loopless regular mat...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Georgia Southern University
2023-01-01
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| Series: | Theory and Applications of Graphs |
| Subjects: | |
| Online Access: | https://digitalcommons.georgiasouthern.edu/tag/vol10/iss2/1/ |
| _version_ | 1797672326876102656 |
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| author | Xiaofeng Wang Taoye Zhang Ju Zhou |
| author_facet | Xiaofeng Wang Taoye Zhang Ju Zhou |
| author_sort | Xiaofeng Wang |
| collection | DOAJ |
| description | Walton and Welsh proved that if a co-loopless regular matroid M does not have a minor in {M(K(3,3)),M∗(K5)}, then M admits a nowhere zero 4-flow. Lai, Li and Poon proved that if M does not have a minor in {M(K5),M∗(K5)}, then M admits a nowhere zero 4-flow. We prove that if a co-loopless regular matroid M does not have a minor in {M((P10)¯3 ),M∗(K5)}, then M admits a nowhere zero 4-flow where (P10)¯3 is the graph obtained from the Petersen graph P10by contracting 3 edges of a perfect matching. As both M(K3,3) and M(K5) are contractions of M((P10)¯3), our result extends the results of Walton and Welsh and Lai, Li and Poon. |
| first_indexed | 2024-03-11T21:28:20Z |
| format | Article |
| id | doaj.art-ebd2062b6e964236b7b62f4e0e9b666e |
| institution | Directory Open Access Journal |
| issn | 2470-9859 |
| language | English |
| last_indexed | 2024-03-11T21:28:20Z |
| publishDate | 2023-01-01 |
| publisher | Georgia Southern University |
| record_format | Article |
| series | Theory and Applications of Graphs |
| spelling | doaj.art-ebd2062b6e964236b7b62f4e0e9b666e2023-09-27T17:07:51ZengGeorgia Southern UniversityTheory and Applications of Graphs2470-98592023-01-011021910.20429/tag.2023.100201On Nowhere Zero 4-Flows in Regular MatroidsXiaofeng WangTaoye ZhangJu ZhouWalton and Welsh proved that if a co-loopless regular matroid M does not have a minor in {M(K(3,3)),M∗(K5)}, then M admits a nowhere zero 4-flow. Lai, Li and Poon proved that if M does not have a minor in {M(K5),M∗(K5)}, then M admits a nowhere zero 4-flow. We prove that if a co-loopless regular matroid M does not have a minor in {M((P10)¯3 ),M∗(K5)}, then M admits a nowhere zero 4-flow where (P10)¯3 is the graph obtained from the Petersen graph P10by contracting 3 edges of a perfect matching. As both M(K3,3) and M(K5) are contractions of M((P10)¯3), our result extends the results of Walton and Welsh and Lai, Li and Poon.https://digitalcommons.georgiasouthern.edu/tag/vol10/iss2/1/nowhere zero flowsregular matroids cycle coversexcluded-minors |
| spellingShingle | Xiaofeng Wang Taoye Zhang Ju Zhou On Nowhere Zero 4-Flows in Regular Matroids Theory and Applications of Graphs nowhere zero flows regular matroids cycle covers excluded-minors |
| title | On Nowhere Zero 4-Flows in Regular Matroids |
| title_full | On Nowhere Zero 4-Flows in Regular Matroids |
| title_fullStr | On Nowhere Zero 4-Flows in Regular Matroids |
| title_full_unstemmed | On Nowhere Zero 4-Flows in Regular Matroids |
| title_short | On Nowhere Zero 4-Flows in Regular Matroids |
| title_sort | on nowhere zero 4 flows in regular matroids |
| topic | nowhere zero flows regular matroids cycle covers excluded-minors |
| url | https://digitalcommons.georgiasouthern.edu/tag/vol10/iss2/1/ |
| work_keys_str_mv | AT xiaofengwang onnowherezero4flowsinregularmatroids AT taoyezhang onnowherezero4flowsinregularmatroids AT juzhou onnowherezero4flowsinregularmatroids |