On the decay of crossing numbers

DOI10.1016/j.jctb.2007.03.005zbMath1131.05033OpenAlexW1974587289MaRDI QIDQ2464150

Jacob Fox, Csaba D. Tóth

Publication date: 10 December 2007

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

Full work available at URL: https://doi.org/10.1016/j.jctb.2007.03.005

zbMATH Keywords

crossing numberembedding methodbisection width

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (6)

Improvement on the decay of crossing numbers ⋮ On the Decay of Crossing Numbers of Sparse Graphs ⋮ The crossing number of \(K_{5,n+1} \setminus e\) ⋮ Nested cycles in large triangulations and crossing-critical graphs ⋮ Improvement on the Crossing Number of Crossing-Critical Graphs ⋮ Improvement on the crossing number of crossing-critical graphs

Cites Work

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• Minimal graphs with crossing number at least \(k\)
• A linear-time algorithm for finding a sparse \(k\)-connected spanning subgraph of a \(k\)-connected graph
• New bounds on crossing numbers
• Compactness results in extremal graph theory
• On a crossing number result of Richter and Thomassen
• Applications of the crossing number
• A Separator Theorem for Planar Graphs
• New lower bound techniques for VLSI
• Crossing-Free Subgraphs
• Improving the crossing lemma by finding more crossings in sparse graphs

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