Undirected graphs of entanglement 2

Authors:
Walid Belkhir;Luigi Santocanale
Affiliations:
Laboratoire d'Informatique Fondamentale de Marseille, Université de Provence;Laboratoire d'Informatique Fondamentale de Marseille, Université de Provence
Venue:
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Year:
2007

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Abstract

Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the problem of deciding whether a graph has entanglement at most k. As this measure is defined by means of games, game theoretic ideas naturally lead to design polynomial algorithms that, for fixed k, decide the problem. Known characterizations of directed graphs of entanglement at most 1 lead, for k = 1, to design even faster algorithms. In this paper we give two distinct characterizations of undirected graphs of entanglement at most 2. With these characterizations at hand, we present a linear time algorithm to decide whether an undirected graph has this property.