Excluding induced subgraphs: Critical graphs

DOI10.1002/rsa.20353zbMath1225.05138OpenAlexW2041545145MaRDI QIDQ3068762

József Balogh, Jane V. Butterfield

Publication date: 17 January 2011

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/rsa.20353

zbMATH Keywords

extremal graphscritical graphsgraph countingstructure of \(H\)-free graphs

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35)

Related Items (12)

THE TYPICAL STRUCTURE OF MAXIMAL TRIANGLE-FREE GRAPHS ⋮ Almost all string graphs are intersection graphs of plane convex sets ⋮ The regularity of almost all edge ideals ⋮ The fine structure of octahedron-free graphs ⋮ The structure of almost all graphs in a hereditary property ⋮ Almost all triple systems with independent neighborhoods are semi-bipartite ⋮ Almost all triangle-free triple systems are tripartite ⋮ Random perfect graphs ⋮ Forbidding induced even cycles in a graph: typical structure and counting ⋮ The typical structure of graphs with no large cliques ⋮ The typical structure of sparse $K_{r+1}$-free graphs ⋮ Almost all string graphs are intersection graphs of plane convex sets

Cites Work

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• The maximum edit distance from hereditary graph properties
• The asymptotic number of graphs not containing a fixed color-critical subgraph
• On the size of hereditary classes of graphs
• The number of graphs without forbidden subgraphs
• The speed of hereditary properties of graphs
• The typical structure of graphs without given excluded subgraphs
• K l+1 -Free Graphs: Asymptotic Structure and a 0-1 Law
• Excluding Induced Subgraphs III: A General Asymptotic
• Almost all Berge Graphs are Perfect
• Projections of Bodies and Hereditary Properties of Hypergraphs

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