Circular flows of nearly Eulerian graphs and vertex‐splitting
Cun Quan Zhang · Journal of Graph Theory · 2002
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 ϵ be a positive real number. We proved that there is a function fS(ϵ) (depends on the surface S and limϵ→0 fS(ϵ)=∞) such that any graph G embedded in S with the odd‐edge connectivity at least fS(ϵ) admits a nowhere‐zero circular (2+ϵ)‐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