Counterexamples to Jaeger's Circular Flow Conjecture

被引：22

作者：

Han, Miaomiao ^{[1
]}

Li, Jiaao ^{[1
]}

Wu, Yezhou ^{[2
]}

Zhang, Cun-Quan ^{[1
]}

机构：

[1] West Virginia Univ, Dept Math, Morgantown, WV 26506 USA

[2] Zhejiang Univ, Ocean Coll, Zhoushan 316021, Zhejiang, Peoples R China

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES B | 2018年 / 131卷

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

Integer flow; Flow index; Jaeger's Conjecture; Circular flow; Counterexample to Jaeger's; Conjecture; Modulo orientations; 3-FLOW CONJECTURE; GRAPHS;

D O I：

10.1016/j.jctb.2018.01.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It was conjectured by Jaeger that every 4p-edge-connected graph admits a modulo (2p + 1)-orientation (and, therefore, admits a nowhere-zero circular (2 + 1/p)-flow). This conjecture was partially proved by Lovasz et al. (2013) [7] for 6p-edge-connected graphs. In this paper, infinite families of counterexamples to Jaeger's conjecture are presented. For p >= 3, there are 4p-edge-connected graphs not admitting modulo (2p + 1)-orientation; for p >= 5, there are (4p + 1)-edgeconnected graphs not admitting modulo (2p + 1)-orientation. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1 / 11

页数：11

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