Schweitzer, Pascal
Towards an Isomorphism Dichotomy for Hereditary Graph Classes
Abstract
In this paper we resolve the complexity of the isomorphism problem on
all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and algorithmic analysis of graphs. First, we develop a methodology to show isomorphism completeness of the isomorphism problem on graph classes by providing a general framework unifying various reduction techniques. Second, we generalize the concept of the modular decomposition to colored graphs, allowing for nonstandard decompositions. We show that, given a suitable decomposition functor, the graph isomorphism problem reduces to checking isomorphism of colored prime graphs. Third, we extend the techniques of bounded color valence and hypergraph isomorphism on hypergraphs of bounded color class size as follows. We say a colored graph has generalized color valence at most k if, after removing all vertices in color classes of size at most k, for each color class C every vertex has at most k neighbors in C or at most k nonneighbors in C. We show that isomorphism of graphs of bounded generalized color valence can be solved in polynomial time.
BibTeX  Entry
@InProceedings{schweitzer:LIPIcs:2015:4951,
author = {Pascal Schweitzer},
title = {{Towards an Isomorphism Dichotomy for Hereditary Graph Classes}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {689702},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897781},
ISSN = {18688969},
year = {2015},
volume = {30},
editor = {Ernst W. Mayr and Nicolas Ollinger},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/4951},
URN = {urn:nbn:de:0030drops49513},
doi = {10.4230/LIPIcs.STACS.2015.689},
annote = {Keywords: graph isomorphism, modular decomposition, bounded color valence, reductions, forbidden induced subgraphs}
}
2015
Keywords: 

graph isomorphism, modular decomposition, bounded color valence, reductions, forbidden induced subgraphs 
Seminar: 

32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

Issue date: 

2015 
Date of publication: 

2015 