@MISC{Eppstein94arboricityand, author = {David Eppstein}, title = {Arboricity and Bipartite Subgraph Listing Algorithms}, year = {1994} }

Share

OpenURL

Abstract

In graphs of bounded arboricity, the total complexity of all maximal complete bipartite subgraphs is O(n). We describe a linear time algorithm to list such subgraphs. The arboricity bound is necessary: for any constant k and any n there exists an n-vertex graph with O(n) edges and (n/ log n) k maximal complete bipartite subgraphs K k,# . # Work supported in part by NSF grant CCR-9258355. 1 Introduction A number of graph algorithms depend on finding all subgraphs of a certain type in a larger graph. For instance, in interval or chordal graphs, a decomposition into maximal cliques is key; such a decomposition can be constructed in linear time [4, 17]. Optimal triangulation construction [3] and certain planar graph computations [8] require a listing of all triangles. Related subgraph isomorphism problems also occur in a wide variety of practical applications [2, 5, 12, 9, 13, 14, 19]. For planar graphs, or more generally for graphs of bounded arboricity, the problem of listing c...