Reduction of the 5-flow conjecture to cyclically 6-edge-connected snarks.

DOI10.1016/S0095-8956(03)00080-7zbMath1033.05067OpenAlexW2030810673MaRDI QIDQ1425113

Martin Kochol

Publication date: 15 March 2004

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0095-8956(03)00080-7

zbMATH Keywords

GirthSnarkCyclic edge-connectivityNowhere-zero 5-flow

Mathematics Subject Classification ID

Connectivity (05C40)

Related Items (23)

Nowhere-zero 5-flows and even (1,2)-factors ⋮ Nowhere-zero 5-flows ⋮ A cyclically 6-edge-connected snark of order 118 ⋮ Decomposition of cubic graphs with cyclic connectivity 5 ⋮ 3-Flows and Combs ⋮ Perfect matchings in highly cyclically connected regular graphs ⋮ Nowhere-zero 5-flows and (1, 2)-factors ⋮ Cubic graphs with colouring defect 3 ⋮ Matrix reduction in a combinatorial computation ⋮ Reduction of the Berge-Fulkerson conjecture to cyclically 5-edge-connected snarks ⋮ Reductions of Matrices Associated with Nowhere-Zero Flows ⋮ Measures of edge-uncolorability of cubic graphs ⋮ A counterexample to the bipartizing matching conjecture ⋮ Parity subgraphs with few common edges and nowhere-zero 5-flow ⋮ Counting nowhere-zero flows on wheels ⋮ Tutte's 5-flow conjecture for highly cyclically connected cubic graphs ⋮ Intersecting 1-factors and nowhere-zero 5-flows ⋮ Linear algebraic approach to an edge-coloring result ⋮ Smallest counterexample to the 5-flow conjecture has girth at least eleven ⋮ Snarks with given real flow numbers ⋮ Decomposition formulas for the flow polynomial ⋮ Nowhere-zero -flows on wheels ⋮ Nowhere‐Zero 5‐Flows On Cubic Graphs with Oddness 4

Cites Work

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• A cyclically 6-edge-connected snark of order 118
• Superposition and constructions of graphs without nowhere-zero \(k\)-flows
• Snarks without small cycles
• A Class Of Abelian Groups
• Infinite Families of Nontrivial Trivalent Graphs Which are Not Tait Colorable
• Hypothetical complexity of the nowhere-zero 5-flow problem
• A Contribution to the Theory of Chromatic Polynomials

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