Smallest counterexample to the 5-flow conjecture has girth at least eleven

DOI10.1016/j.jctb.2009.12.001zbMath1211.05055OpenAlexW2003279860MaRDI QIDQ974466

Martin Kochol

Publication date: 3 June 2010

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

Full work available at URL: https://doi.org/10.1016/j.jctb.2009.12.001

zbMATH Keywords

girthpermutation grouprank of a matrixnowhere-zero 5-flow

Mathematics Subject Classification ID

Graph theory (05C99) Flows in graphs (05C21)

Related Items (8)

Nowhere-zero 5-flows ⋮ Matrix reduction in a combinatorial computation ⋮ Reduction of the Berge-Fulkerson conjecture to cyclically 5-edge-connected snarks ⋮ Measures of edge-uncolorability of cubic graphs ⋮ Counting nowhere-zero flows on wheels ⋮ The Chvátal-Erdős condition for group connectivity in graphs ⋮ Avoiding 5-Circuits in 2-Factors of Cubic Graphs ⋮ Nowhere‐Zero 5‐Flows On Cubic Graphs with Oddness 4

Cites Work

• Counting nowhere-zero flows on wheels
• A cyclically 6-edge-connected snark of order 118
• Reduction of the 5-flow conjecture to cyclically 6-edge-connected snarks.
• Superposition and constructions of graphs without nowhere-zero \(k\)-flows
• Snarks without small cycles
• Matrix reduction in a combinatorial computation
• Restrictions on smallest counterexamples to the 5-flow conjecture
• Decomposition formulas for the flow polynomial
• A Class Of Abelian Groups
• Infinite Families of Nontrivial Trivalent Graphs Which are Not Tait Colorable
• A Contribution to the Theory of Chromatic Polynomials
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