Small snarks with large oddness

zbMath1308.05051arXiv1212.3641MaRDI QIDQ2260625

Robert Lukot'ka, Edita Máčajová, Ján Mazák, Martin Škoviera

Publication date: 11 March 2015

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.3641

zbMATH Keywords

cubic graphoddnesssnarkresistance

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Coloring of graphs and hypergraphs (05C15) Connectivity (05C40)

Related Items (15)

5-Cycle Double Covers, 4-Flows, and Catlin Reduction ⋮ Oddness to resistance ratios in cubic graphs ⋮ Even cycle decompositions of index 3 by a novel coloring technique ⋮ Girth, oddness, and colouring defect of snarks ⋮ Rotationally symmetric snarks from voltage graphs ⋮ Coverings of cubic graphs and 3-edge colorability ⋮ On \(S\)-packing edge-colorings of cubic graphs ⋮ Measures of edge-uncolorability of cubic graphs ⋮ Weak oddness as an approximation of oddness and resistance in cubic graphs ⋮ On the smallest snarks with oddness 4 and connectivity 2 ⋮ Berge-Fulkerson coloring for some families of superposition snarks ⋮ Short Cycle Covers of Cubic Graphs and Intersecting 5-Circuits ⋮ The smallest nontrivial snarks of oddness 4 ⋮ Short Cycle Covers on Cubic Graphs by Choosing a 2-Factor ⋮ Morphology of small snarks

Cites Work

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• Generation and properties of snarks
• Covering weighted graphs by even subgraphs
• The number of cycles in 2-factors of cubic graphs
• Classification and characterizations of snarks
• Superposition and constructions of graphs without nowhere-zero \(k\)-flows
• On the smallest snarks with oddness 4 and connectivity 2
• Double covers of cubic graphs with oddness 4
• Measurements of edge-uncolorability
• Five cycle double covers of some cubic graphs
• Snarks without small cycles
• Cycles Intersecting Edge-Cuts of Prescribed Sizes
• The NP-Completeness of Edge-Coloring
• Almost all cubic graphs are Hamiltonian
• Maximum matching and a polyhedron with 0,1-vertices

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