Colour-critical graphs and hypergraphs

DOI10.1016/0095-8956(74)90057-4zbMath0269.05117OpenAlexW1971849303MaRDI QIDQ2563172

Bjarne Toft

Publication date: 1974

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0095-8956(74)90057-4

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Coloring of graphs and hypergraphs (05C15)

Related Items (23)

On the colorability of \(m\)-composed graphs ⋮ Subgraphs of colour-critical graphs ⋮ THE ADJACENCY GRAPH DETERMINED BY A GIVEN HYPERGRAPH ⋮ On constructive methods in the theory of colour-critical graphs ⋮ The complexity of generalized graph colorings ⋮ A note on \(\Delta\)-critical graphs ⋮ The enumeration problem for color critical linear hypergraphs ⋮ Concepts on coloring of cluster hypergraphs with application ⋮ Critical hypergraphs for the weak chromatic number ⋮ Graph coloring satisfying restraints ⋮ Graph properties and hypergraph colourings ⋮ A vertex critical graph without critical edges ⋮ Partitioning sparse graphs into an independent set and a forest of bounded degree ⋮ A Brooks type theorem for the maximum local edge connectivity ⋮ Box and Segment Intersection Graphs with Large Girth and Chromatic Number ⋮ A broken cycle theorem for the restrained chromatic function ⋮ Amenable colorings ⋮ Complete colourings of hypergraphs ⋮ A Brooks-type result for sparse critical graphs ⋮ Restraints permitting the largest number of colourings ⋮ On the minimal number of edges in color-critical graphs ⋮ A list version of Dirac's theorem on the number of edges in colour-critical graphs ⋮ Sparse colour-critical hypergraphs

Cites Work

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• On chromatic number of graphs and set-systems
• On chromatic number of finite set-systems
• On odd circuits in chromatic graphs
• On A Combinatorial Problem of Erdös
• $B$-sets and coloring problems
• Self-dual configurations and regular graphs
• The structure of k-chromatic graphs
• Paths and Circuits in Critical Graphs

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