论文信息 - Nowhere‐Zero 5‐Flows On Cubic Graphs with Oddness 4

Nowhere‐Zero 5‐Flows On Cubic Graphs with Oddness 4

Tutte's 5-flow conjecture from 1954 states that every bridgeless graph has a nowhere-zero 5-flow. It suffices to prove the conjecture for cyclically 6-edge-connected cubic graphs. We prove that every cyclically 6-edge-connected cubic graph with oddness at most 4 has a nowhere-zero 5-flow. This implies that every minimum counterexample to the 5-flow conjecture has oddness at least 6.

Eckhard Steffen | Giuseppe Mazzuoccolo | G. Mazzuoccolo | E. Steffen

[1] Paul Seymour,et al. Nowhere-zero flows , 1996 .

[2] Martin Kochol,et al. Reduction of the 5-Flow Conjecture to cyclically 6-edge-connected snarks , 2004, J. Comb. Theory, Ser. B.

[3] Eckhard Steffen. Tutte's 5-flow conjecture for highly cyclically connected cubic graphs , 2007, Electron. Notes Discret. Math..

[4] F. Jaeger,et al. Balanced valuations and flows in multigraphs , 1976 .

[5] J. Bondy. Balanced colourings and the four colour conjecture , 1972 .

[6] Paul D. Seymour,et al. Nowhere-zero 6-flows , 1981, J. Comb. Theory, Ser. B.

[7] Roland Häggkvist,et al. Double covers of cubic graphs with oddness 4 , 2005, J. Comb. Theory, Ser. B.

[8] Martin Kochol,et al. Five Cycle Double Covers of Some Cubic Graphs , 1995, J. Comb. Theory, Ser. B.

[9] J. Petersen. Die Theorie der regulären graphs , 1891 .

[10] Edita Mácajová,et al. Sparsely intersecting perfect matchings in cubic graphs , 2014, Comb..

[11] W. T. Tutte,et al. A Contribution to the Theory of Chromatic Polynomials , 1954, Canadian Journal of Mathematics.

[12] Martin Kochol,et al. Smallest counterexample to the 5-flow conjecture has girth at least eleven , 2010, J. Comb. Theory, Ser. B.