TY - JOUR
T1 - On Nowhere Zero 4-Flows in Regular Matroids
AU - Wang, Xiaofeng
AU - Zhang, Taoye
AU - Zhou, Ju
N1 - Publisher Copyright:
© 2023 Georgia Southern University. All rights reserved.
PY - 2023
Y1 - 2023
N2 - 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)3̄), M∗(K5)}, then M admits a nowhere zero 4-flow where (P10)3̄ 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)3̄), our result extends the results of Walton and Welsh and Lai, Li and Poon.
AB - 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)3̄), M∗(K5)}, then M admits a nowhere zero 4-flow where (P10)3̄ 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)3̄), our result extends the results of Walton and Welsh and Lai, Li and Poon.
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U2 - 10.20429/tag.2023.100201
DO - 10.20429/tag.2023.100201
M3 - Article
AN - SCOPUS:85174814338
SN - 2470-9859
VL - 10
JO - Theory and Applications of Graphs
JF - Theory and Applications of Graphs
IS - 2
M1 - 1
ER -