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Nowhere-zero 3-flows in locally connected graphs

✍ Scribed by Hong-Jian Lai

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
91 KB
Volume
42
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

Let G be a graph. For each vertex v ∈V(G), N~v~ denotes the subgraph induces by the vertices adjacent to v in G. The graph G is locally k‐edge‐connected if for each vertex v ∈V(G), N~v~ is k‐edge‐connected. In this paper we study the existence of nowhere‐zero 3‐flows in locally k‐edge‐connected graphs. In particular, we show that every 2‐edge‐connected, locally 3‐edge‐connected graph admits a nowhere‐zero 3‐flow. This result is best possible in the sense that there exists an infinite family of 2‐edge‐connected, locally 2‐edge‐connected graphs each of which does not have a 3‐NZF. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 211–219, 2003

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