On Nowhere Zero 4-Flows in Regular Matroids

Xiaofeng Wang, Taoye Zhang, Ju Zhou

Research output: Contribution to journalArticlepeer-review

Abstract

Walton and Welsh proved that if a coloopless regular matroid M does not have a minor in {M(K3,3), 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 coloopless regular matroid M does not have a minor in {M((P10)), M(K5)}, then M admits a nowhere zero 4-flow where (P10) is the graph obtained from the Petersen graph P10 by contracting 3 edges of a perfect matching. As both M(K3,3) and M(K5) are contractions of M((P10)), our result extends the results of Walton and Welsh and Lai, Li and Poon.

Original languageEnglish (US)
Article number1
JournalTheory and Applications of Graphs
Volume10
Issue number2
DOIs
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Numerical Analysis
  • Discrete Mathematics and Combinatorics

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