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Circular flows of nearly Eulerian graphs and vertex‐splitting
Authors:Cun Quan Zhang
Abstract:The odd edge connectivity of a graph G, denoted by λo(G), is the size of a smallest odd edge cut of the graph. Let S be any given surface and ? be a positive real number. We proved that there is a function fS(?) (depends on the surface S and lim?→0 fS(?)=∞) such that any graph G embedded in S with the odd‐edge connectivity at least fS(?) admits a nowhere‐zero circular (2+?)‐flow. Another major result of the work is a new vertex splitting lemma which maintains the old edge connectivity and graph embedding. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 147–161, 2002
Keywords:circular flow  nearly Eulerian graphs  vertex splitting  integer flow
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