K 4 -free and C6¯-free Planar Matching Covered Graphs

DOI10.1002/jgt.21882zbMath1339.05318OpenAlexW1764061692MaRDI QIDQ2811192

Nishad Kothari, U. S. R. Murty

Publication date: 10 June 2016

Published in: Journal of Graph Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/jgt.21882

zbMATH Keywords

matching covered graphsbricksear-decompositionsbi-subdivisionconformal subgraphs

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (6)

On Two Unsolved Problems Concerning Matching Covered Graphs ⋮ Birkhoff--von Neumann Graphs that are PM-Compact ⋮ Matching extension in prism graphs ⋮ On essentially 4-edge-connected cubic bricks ⋮ \(b\)-invariant edges in essentially 4-edge-connected near-bipartite cubic bricks ⋮ Colouring non-even digraphs

Cites Work

• Ear-decompositions of matching-covered graphs
• Brick decompositions and the matching rank of graphs
• Matching structure and the matching lattice
• Proof of Toft's conjecture: Every graph containing no fully odd \(K_4\) is 3-colorable
• Matching covered graphs and subdivisions of \(K_ 4\) and \(\bar C_ 6\)
• How to build a brick
• Generating bricks
• 2-Isomorphic Graphs
• Totally odd \(K_4\)-subdivisions in 4-chromatic graphs

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