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

数学与统计学院

Northwestern Polytechnical University Xian
Shangluo University

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	1653-1664
页数	12
期刊	Acta Mathematica Sinica, English Series
卷	38
期	9
DOI	https://doi.org/10.1007/s10114-022-1006-9
出版状态	已出版 - 9月 2022

访问文件

10.1007/s10114-022-1006-9

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{ed89d3ff840442fa8a3594c1faba3065,

title = "Note on Integer 4-flows in Graphs",

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.",

keywords = "05C21, circuit, Integer 4-flow, modulo 4-flow",

author = "Xiao Wang and You Lu and Zhang, \{Sheng Gui\}",

note = "Publisher Copyright: {\textcopyright} 2022, Springer-Verlag GmbH Germany \& The Editorial Office of AMS.",

year = "2022",

month = sep,

doi = "10.1007/s10114-022-1006-9",

language = "英语",

volume = "38",

pages = "1653--1664",

journal = "Acta Mathematica Sinica, English Series",

issn = "1439-8516",

publisher = "Springer Verlag",

number = "9",

}

TY - JOUR

T1 - Note on Integer 4-flows in Graphs

AU - Wang, Xiao

AU - Lu, You

AU - Zhang, Sheng Gui

PY - 2022/9

Y1 - 2022/9

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.

KW - 05C21

KW - circuit

KW - Integer 4-flow

KW - modulo 4-flow

UR - https://www.scopus.com/pages/publications/85139748965

U2 - 10.1007/s10114-022-1006-9

DO - 10.1007/s10114-022-1006-9

M3 - 文章

AN - SCOPUS:85139748965

SN - 1439-8516

VL - 38

SP - 1653

EP - 1664

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 9

ER -

Note on Integer 4-flows in Graphs

摘要

访问文件

其它文件与链接

指纹

引用此