Note on Integer 4-flows in Graphs

Xiao Wang; You Lu; Sheng Gui Zhang

doi:10.1007/s10114-022-1006-9

Note on Integer 4-flows in Graphs

Xiao Wang, You Lu, Sheng Gui Zhang

School of Mathematics and Statistics

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

1 Scopus citations

Abstract

Let G be a bridgeless graph and C be a circuit in G. To find a shorter circuit cover of G, Fan proposed a conjecture that if G/C admits a nowhere-zero 4-flow, then G admits a 4-flow (D, f) such that E(G) E(C) ⊆ supp(f) and |supp(f)∩E(C)|>34|E(C)|, and showed that the conjecture holds if ∣E(C)∣≤ 19 [Combinatorica, 37, 1097–1112 (2017)]. In this paper, we prove that the conjecture holds if ∣E(C)∣≤ 27.

Original language	English
Pages (from-to)	1653-1664
Number of pages	12
Journal	Acta Mathematica Sinica, English Series
Volume	38
Issue number	9
DOIs	https://doi.org/10.1007/s10114-022-1006-9
State	Published - Sep 2022

Keywords

05C21
circuit
Integer 4-flow
modulo 4-flow

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10.1007/s10114-022-1006-9

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T1 - Note on Integer 4-flows in Graphs

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AU - Zhang, Sheng Gui

PY - 2022/9

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N2 - Let G be a bridgeless graph and C be a circuit in G. To find a shorter circuit cover of G, Fan proposed a conjecture that if G/C admits a nowhere-zero 4-flow, then G admits a 4-flow (D, f) such that E(G) E(C) ⊆ supp(f) and |supp(f)∩E(C)|>34|E(C)|, and showed that the conjecture holds if ∣E(C)∣≤ 19 [Combinatorica, 37, 1097–1112 (2017)]. In this paper, we prove that the conjecture holds if ∣E(C)∣≤ 27.

AB - Let G be a bridgeless graph and C be a circuit in G. To find a shorter circuit cover of G, Fan proposed a conjecture that if G/C admits a nowhere-zero 4-flow, then G admits a 4-flow (D, f) such that E(G) E(C) ⊆ supp(f) and |supp(f)∩E(C)|>34|E(C)|, and showed that the conjecture holds if ∣E(C)∣≤ 19 [Combinatorica, 37, 1097–1112 (2017)]. In this paper, we prove that the conjecture holds if ∣E(C)∣≤ 27.

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Note on Integer 4-flows in Graphs

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