26 research outputs found
Efficient enumeration of maximal split subgraphs and sub-cographs and related classes
In this paper, we are interested in algorithms that take in input an
arbitrary graph , and that enumerate in output all the (inclusion-wise)
maximal "subgraphs" of which fulfil a given property . All over this
paper, we study several different properties , and the notion of subgraph
under consideration (induced or not) will vary from a result to another.
More precisely, we present efficient algorithms to list all maximal split
subgraphs, sub-cographs and some subclasses of cographs of a given input graph.
All the algorithms presented here run in polynomial delay, and moreover for
split graphs it only requires polynomial space. In order to develop an
algorithm for maximal split (edge-)subgraphs, we establish a bijection between
the maximal split subgraphs and the maximal independent sets of an auxiliary
graph. For cographs and some subclasses , the algorithms rely on a framework
recently introduced by Conte & Uno called Proximity Search. Finally we consider
the extension problem, which consists in deciding if there exists a maximal
induced subgraph satisfying a property that contains a set of prescribed
vertices and that avoids another set of vertices. We show that this problem is
NP-complete for every "interesting" hereditary property . We extend the
hardness result to some specific edge version of the extension problem
The Complexity of Surjective Homomorphism Problems -- a Survey
We survey known results about the complexity of surjective homomorphism
problems, studied in the context of related problems in the literature such as
list homomorphism, retraction and compaction. In comparison with these
problems, surjective homomorphism problems seem to be harder to classify and we
examine especially three concrete problems that have arisen from the
literature, two of which remain of open complexity
Proximity Search for Maximal Subgraph Enumeration
International audienc
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum