The Erdős–Rothschild problem on edge-colourings with forbidden monochromatic cliques

DOI10.1017/S0305004116001031zbMath1371.05095arXiv1605.05074MaRDI QIDQ5360466

Oleg Pikhurko, Katherine Staden, Zelealem B. Yilma

Publication date: 28 September 2017

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.05074

zbMATH Keywords

stability theorem for complete multipartite graphs

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (19)

Edge-colorings of graphs avoiding complete graphs with a prescribed coloring ⋮ Stability for the Erdős-Rothschild problem ⋮ Remarks on an edge-coloring problem ⋮ Integer colorings with no rainbow \(k\)-term arithmetic progression ⋮ Counting H-free orientations of graphs ⋮ Improved Bound on the Maximum Number of Clique-Free Colorings with Two and Three Colors ⋮ On graphs with a large number of edge-colorings avoiding a rainbow triangle ⋮ On the maximum number of integer colourings with forbidden monochromatic sums ⋮ Counting orientations of graphs with no strongly connected tournaments ⋮ On Two Problems in Ramsey--Turán Theory ⋮ A Rainbow Erdös--Rothschild Problem ⋮ Exact solutions to the Erdős-Rothschild problem ⋮ Colourings without monochromatic disjoint pairs ⋮ Edge colorings of graphs without monochromatic stars ⋮ An extension of the rainbow Erdős-Rothschild problem ⋮ Rainbow Erdös--Rothschild Problem for the Fano Plane ⋮ Counting Gallai 3-colorings of complete graphs ⋮ The number of Gallai \(k\)-colorings of complete graphs ⋮ Colouring set families without monochromatic \(k\)-chains

Cites Work

• Edge-colorings avoiding fixed rainbow stars
• A structural result for hypergraphs with many restricted edge colorings
• A coloring problem for intersecting vector spaces
• Set-coloring of edges and multigraph Ramsey numbers
• Edge-colorings avoiding a fixed matching with a prescribed color pattern
• Edge-colorings of graphs avoiding complete graphs with a prescribed coloring
• A remark on the number of edge colorings of graphs
• The number of oriantations having no fixed tournament
• Edge-colorings of graphs avoiding fixed monochromatic subgraphs with linear Turán number
• Kneser Colorings of Uniform Hypergraphs
• Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size
• The maximum number of K ₃ -free and K ₄ -free edge 4-colorings
• On Colourings of Hypergraphs Without Monochromatic Fano Planes
• THE NUMBER OF EDGE COLORINGS WITH NO MONOCHROMATIC CLIQUES
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