Premium
Nowhere‐zero 3‐flows in locally connected graphs
Author(s) -
Lai HongJian
Publication year - 2003
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.10085
Subject(s) - combinatorics , mathematics , vertex (graph theory) , connectivity , graph , vertex connectivity , discrete mathematics
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