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Nowhere zero 4‐flow in regular matroids
Author(s) -
Lai HongJian,
Li Xiangwen,
Poon Hoifung
Publication year - 2005
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20075
Subject(s) - matroid , combinatorics , mathematics , minor (academic) , zero (linguistics) , conjecture , graph , graphic matroid , discrete mathematics , signed graph , linguistics , philosophy , political science , law
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