On Nowhere Zero 4-Flows in Regular Matroids

Authors

Xiaofeng Wang, Indiana University NorthwestFollow
Taoye Zhang, Penn State ScrantonFollow
Ju Zhou, Kutztown University of PennsylvaniaFollow

Publication Date

September 2023

Abstract

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.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Wang, Xiaofeng; Zhang, Taoye; and Zhou, Ju (2023) "On Nowhere Zero 4-Flows in Regular Matroids," Theory and Applications of Graphs: Vol. 10: Iss. 2, Article 1.
DOI: 10.20429/tag.2023.100201
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol10/iss2/1