Nowhere-zero 3-flows in locally connected graphs

  • Authors:

  • Hong-Jian Lai

  • Affiliations:

  • Department of Mathematics, West Virginia University, Morgantown, WV 26506

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2003

Quantified Score

Hi-index 0.00

Visualization

Abstract

Let G be a graph. For each vertex v ∈V(G), Nv 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), Nv 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