A Relative of Hadwiger's Conjecture

DOI10.1137/141002177zbMath1328.05063arXiv1407.5236OpenAlexW2109001973WikidataQ122950786 ScholiaQ122950786MaRDI QIDQ3461983

Dong Yeap Kang, Katherine Edwards, Sang-il Oum, P. D. Seymour, Jae-Hoon Kim

Publication date: 4 January 2016

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.5236

zbMATH Keywords

minorHadwiger's conjectureimproper coloring

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Coloring of graphs and hypergraphs (05C15) Graph minors (05C83) Vertex degrees (05C07)

Related Items (15)

Clustered colouring of graph classes with bounded treedepth or pathwidth ⋮ Improved bound for improper colourings of graphs with no odd clique minor ⋮ Clustered 3-colouring graphs of bounded degree ⋮ Clustered variants of Hajós' conjecture ⋮ Defective coloring of hypergraphs ⋮ Sparse critical graphs for defective DP-colorings ⋮ Partitioning \(H\)-minor free graphs into three subgraphs with no large components ⋮ On 2-defective DP-colorings of sparse graphs ⋮ Defective DP-colorings of sparse multigraphs ⋮ Defective DP-colorings of sparse simple graphs ⋮ Partitioning \(H\)-minor free graphs into three subgraphs with no large components ⋮ Improper colouring of graphs with no odd clique minor ⋮ Defective and clustered choosability of sparse graphs ⋮ Hadwiger’s Conjecture ⋮ Immersion and clustered coloring

Cites Work

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• Contractibility and the Hadwiger conjecture
• Lower bound of the Hadwiger number of graphs by their average degree
• A relaxed Hadwiger's conjecture for list colorings
• Hajos' graph-coloring conjecture: Variations and counterexamples
• Hadwiger's conjecture for \(K_ 6\)-free graphs
• Partitioning into graphs with only small components
• The extremal function for complete minors
• Defective coloring revisited
• An extremal function for contractions of graphs

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