Nowhere-zero 6-flows

  title={Nowhere-zero 6-flows},
  author={Paul D. Seymour},
  journal={J. Comb. Theory, Ser. B},
  • P. Seymour
  • Published 1 April 1981
  • Mathematics
  • J. Comb. Theory, Ser. B
Nowhere-zero 5-flows
Hypothetical complexity of the nowhere-zero 5-flow problem
We show that if the well-known 5-Flow Conjecture of Tutte is not true, then the problem to determine whether a (cubic) graph admits a nowhere-zero 5-flow is NP-complete. © 1998 John Wiley & Sons,
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
Exponentially Many Nowhere-Zero ℤ3-, ℤ4-, and ℤ6-Flows
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
Nowhere-zero integral flows on a bidirected graph
  • A. Bouchet
  • Mathematics, Engineering
    J. Comb. Theory, Ser. B
  • 1983
A new proof of Seymour's 6-flow theorem
Intersecting 1-factors and nowhere-zero 5-flows
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.
Degree sum and nowhere-zero 3-flows


Flows and generalized coloring theorems in graphs
  • F. Jaeger
  • Mathematics
    J. Comb. Theory, Ser. B
  • 1979
A Class Of Abelian Groups
  • W. T. Tutte
  • Mathematics, Philosophy
    Canadian Journal of Mathematics
  • 1956
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
A contribution to the theory of chromatic polynomials
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,
Eine gemeinsame Basis für die Theorie der Eulerschen Graphen und den Satz von Petersen
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