Efficient Algorithms for Subgraph Listing

Subgraph isomorphism is a fundamental problem in graph theory. In this paper we focus on listing subgraphs isomorphic to a given pattern graph. First, we look at the algorithm due to Chiba and Nishizeki for listing complete subgraphs of fixed size, and show that it cannot be extended to general subg...

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Bibliographic Details
Published in:Algorithms Vol. 7; no. 2; pp. 243 - 252
Main Authors: Zechner, Niklas, Lingas, Andrzej
Format: Journal Article
Language:English
Published: Basel MDPI AG 2014
Subjects:
Algorithms
Boolean algebra
Clique
Graph theory
Graphs
Isomorphism
Output-sensitive algorithm
Subgraph
Subgraph isomorphism
Subgraph listing
Time complexity
Triangle
Triangles
ISSN:1999-4893, 1999-4893
Online Access:Get full text
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Summary:Subgraph isomorphism is a fundamental problem in graph theory. In this paper we focus on listing subgraphs isomorphic to a given pattern graph. First, we look at the algorithm due to Chiba and Nishizeki for listing complete subgraphs of fixed size, and show that it cannot be extended to general subgraphs of fixed size. Then, we consider the algorithm due to Ga̧sieniec et al. for finding multiple witnesses of a Boolean matrix product, and use it to design a new output-sensitive algorithm for listing all triangles in a graph. As a corollary, we obtain an output-sensitive algorithm for listing subgraphs and induced subgraphs isomorphic to an arbitrary fixed pattern graph.
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ISSN:1999-4893
1999-4893
DOI:10.3390/a7020243