On the minimum number of arcs in \(k\)-dicritical oriented graphs

DOI10.1137/23M1553753zbMATH Open1542.05063MaRDI QIDQ6561323

Clément Rambaud, Pierre Aboulker, Thomas Bellitto, Frédéric Havet

Publication date: 25 June 2024

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

zbMATH Keywords

digraphdichromatic number

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Enumeration in graph theory (05C30) Coloring of graphs and hypergraphs (05C15) Directed graphs (digraphs), tournaments (05C20)

Cites Work

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• Ore's conjecture for \(k=4\) and Grötzsch's theorem
• Ore's conjecture on color-critical graphs is almost true
• The edge density of critical digraphs
• Decomposing a graph into forests
• Eigenvalues and colorings of digraphs
• The 3 and 4-dichromatic tournaments of minimum order
• The dichromatic number of a digraph
• The minimum number of edges in 4-critical digraphs of given order
• Hajós and Ore constructions for digraphs
• On the minimum number of edges in triangle-free 5-critical graphs
• A Theorem of R. L. Brooks and a Conjecture of H. Hadwiger
• The circular chromatic number of a digraph
• On the Minimum Edge‐Density of 4‐Critical Graphs of Girth Five
• A Property of 4-Chromatic Graphs and some Remarks on Critical Graphs
• On the number of edges in colour-critical graphs and hypergraphs
• The smallest 5-chromatic tournament
• Various bounds on the minimum number of arcs in a \(k\)-dicritical digraph

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