Let G be a 2-edge-connected graph with o vertices of odd degree. It is well-known that one should (and can) add o 2 edges to G in order to obtain a graph which admits a nowhere-zero 2-flow. We prove… Expand

We prove that, in several settings, a graph has exponentially many nowhere-zero flows. These results may be seen as a counting alternative to the well-known proofs of existence of ℤ3-, ℤ4-, and… Expand

A cyclically n-edge-connected cubic graph G has a nowhere-zero 5-flow if (1) n≤6 and μ2(G)≤2 or (2) if n≥5μ2 (G)−3, and the minimum number k such that two 1-factors of G intersect in k edges is k.Expand

1. Introduction. If M is any finite set we define a chain on M as a mapping f of M into the set of ordinary integers. If a ∈ M then f(a) is the coefficient of a in the chain f. The set of all a ∈ M… Expand

Summary Two polynomials θ(G, n) and ϕ(G, n) connected with the colourings of a graph G or of associated maps are discussed. A result believed to be new is proved for the lesser-known polynomial ϕ(G,… Expand

The main result states: Lete1,e2,e3 be three lines incident to the pointv (degv≥4) of the connected bridgeless graphG such thate1 ande3 belong to different blocks ifv is a cutpoint. “Split the… Expand