Circular flows of nearly Eulerian graphs and vertex-splitting

  • Authors:

  • Cun Quan Zhang

  • Affiliations:

  • Department of Mathematics, P. O. Box 6310, West Virginia University, Morgantown, West Virginia 26506

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2002

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Abstract

The odd edge connectivity of a graph G, denoted byλo(G), is the size of a smallestodd edge cut of the graph. Let S be any given surface andε be a positive real number. We proved that there is afunction fS(ε) (depends on thesurface S and limε➝0fS(ε)=∞) such that any graphG embedded in S with the odd-edge connectivity atleast fS(ε) admits a nowhere-zerocircular (2+ε)-flow. Another major result of the work is anew vertex splitting lemma which maintains the old edgeconnectivity and graph embedding. © 2002 Wiley Periodicals,Inc. J Graph Theory 40: 147161, 2002