Discrete Mathematics - First Japan Conference on Graph Theory and Applications
Polynomial space polynomial delay algorithms for listing families of graphs
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Computers and Operations Research
Isomorph-free exhaustive generation
Journal of Algorithms
Variable neighborhood search for extremal graphs: 1 the AutoGraphiX system
Discrete Mathematics
A Polynomial Algorithm for Recognizing Perfect Graphs
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Irredundance perfect and P6-free graphs
Journal of Graph Theory
Proof of a conjecture on irredundance perfect graphs
Journal of Graph Theory
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Given a class of graphs F, a forbidden subgraph characterization (FSC) is a set of graphs H such that a graph G belongs to F if and only if no graph of H is isomorphic to an induced subgraph of G. FSCs play a key role in graph theory, and are at the center of many important results obtained in that field. In this paper, we present novel methods that automate the generation of conjectures on FSCs. Since most classes of graphs do not have such characterization, we also describe methods to find less restrictive results in the form of necessary or sufficient conditions to characterize a class of graphs with forbidden subgraphs. Furthermore, while these methods require to explore a possibly infinite search space, we present an enumerative technique that guarantees the discovery of characterizations involving forbidden subgraphs with a limited number of vertices. Another technique, which enables the discovery of characterizations with much larger subgraphs through the use of a heuristic search, is also described. In our experiments, we use these methods to find new theorems on the characterization of well-known graph classes.