Abstract
Let G be a bridgeless cubic graph, and μ 2(G) the minimum number k such that two 1-factors of G intersect in k edges. A cyclically n-edge-connected cubic graph G has a nowhere-zero 5-flow if (1) n≥6 and μ 2(G)≤2 or (2) if n≥5μ 2(G)−3.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. A. Bondy: Balanced Colourings and the four colour conjecture, Proc. Amer. Math. Soc. 33 (1972), 241–244.
F. Jaeger: Balanced valuations and flows in multigraphs, Proc. Amer. Math. Soc. 55 (1975), 237–242.
F. Jaeger: Nowhere-zero flow problems, in: L. W. Beineke, R. J. Wilson eds., Topics in Graph Theory 3, Academic Press, London (1988), 70–95.
M. Kochol: Reduction of the 5-flow conjecture to cyclically 6-edge-connected snarks, J. Combin. Theory, Ser. B 90 (2004), 139–145.
P. D. Seymour: Nowhere-zero 6-flows, J. Combin. Theory, Ser. B 30 (1981), 130–135.
P. D. Seymour: Nowhere-zero flows, in: Handbook of Combinatorics (Vol. 1), R. L. Graham, M. Grötschel, L. Lovász (eds.), Elsevier Science B.V. Amsterdam (1995), 289–299.
E. Steffen: Tutte’s 5-flow conjecture for highly cyclically connected cubic graphs, Discrete Math. 310 (2010), 385–389.
W. T. Tutte: A contribution to the theory of chromatic polynomials, Canadian J. Math. 6 (1954), 80–91.
