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：
中国国家自然科学基金; 美国国家科学基金会;
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.
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页码：1 / 11
页数：11
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