On Nowhere Zero 4-Flows in Regular Matroids

Xiaofeng Wang; Taoye Zhang; Ju Zhou

doi:10.20429/tag.2023.100201

On Nowhere Zero 4-Flows in Regular Matroids

Xiaofeng Wang
, Taoye Zhang
, Ju Zhou

Penn State Scranton

Research output: Contribution to journal › Article › peer-review

Abstract

Walton and Welsh proved that if a coloopless 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 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(K_3,3) and M(K₅) are contractions of M((P₁₀)_3̄), our result extends the results of Walton and Welsh and Lai, Li and Poon.

Original language	English (US)
Article number	1
Journal	Theory and Applications of Graphs
Volume	10
Issue number	2
DOIs	https://doi.org/10.20429/tag.2023.100201
State	Published - 2023

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Numerical Analysis
Discrete Mathematics and Combinatorics

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title = "On Nowhere Zero 4-Flows in Regular Matroids",

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){\=3}), M∗(K5)\}, then M admits a nowhere zero 4-flow where (P10){\=3} 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){\=3}), our result extends the results of Walton and Welsh and Lai, Li and Poon.",

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doi = "10.20429/tag.2023.100201",

language = "English (US)",

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journal = "Theory and Applications of Graphs",

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T1 - On Nowhere Zero 4-Flows in Regular Matroids

AU - Wang, Xiaofeng

AU - Zhang, Taoye

AU - Zhou, Ju

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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DO - 10.20429/tag.2023.100201

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JO - Theory and Applications of Graphs

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ER -

On Nowhere Zero 4-Flows in Regular Matroids

Abstract

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