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Nowhere zero 4-flow in regular matroids

✍ Scribed by Hong-Jian Lai; Xiangwen Li; Hoifung Poon

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 96 KB
Volume: 49
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20075

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✦ Synopsis

Abstract

Jensen and Toft 8 conjectured that every 2‐edge‐connected graph without a K~5~‐minor has a nowhere zero 4‐flow. Walton and Welsh 19 proved that if a coloopless regular matroid M does not have a minor in {M(K~3,3~), M*(K~5~)}, then M admits a nowhere zero 4‐flow. In this note, we prove that if a coloopless regular matroid M does not have a minor in {M(K~5~), M*(K~5~)}, then M admits a nowhere zero 4‐flow. Our result implies the Jensen and Toft conjecture. © 2005 Wiley Periodicals, Inc. J Graph Theory

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