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Abstract: It is well known that any planar graph contains at most O(n) complete subgraphs. We extend this to an exact characterization: G occurs O(n) times as a subgraph of any planar graph, if and only if G is threeconnected. Even more generally, G occurs O(n) times as a subgraph of the K b,c -free graphs, b # c, if and only if G is c-connected; G occurs O(n) times as a subgraph of the K a -free graphs if and only if G is (a - 1)-connected. Our results use a simple Ramsey-theoretic lemma that ... (Update)
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BibTeX entry: (Update)
@misc{ eppstein-connectivity,
author = "David Eppstein",
title = "Connectivity, Graph Minors, and Subgraph Multiplicity",
url = "citeseer.ist.psu.edu/258865.html" }
Citations (may not include all citations):117 Mesh generation and optimal triangulation - Bern, Eppstein
41 Arboricity and subgraph listing algorithms (context) - Chiba, Nishizeki - 1985
36 The book thickness of a graph (context) - Bernhart, Kainen - 1979
22 Planar orientations with low out-degree and compaction of ad.. - Chrobak, Eppstein - 1991
12 A linear-time algorithm for testing the inscribability of tr.. - Dillencourt, Smith - 1991
4 The clique problem for planar graphs (context) - Papadimitriou, Yannakakis - 1981
1 Koninklijke Nederlandse Akademie van Wetenschappen (context) - Tutte, of et al. - 1961
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