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Recursive algorithm for parity games requires exponential time

Oliver Friedmann (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

This paper presents a new lower bound for the recursive algorithm for solving parity games which is induced by the constructive proof of memoryless determinacy by Zielonka. We outline a family of games of linear size on which the algorithm requires exponential time.

Recursive algorithm for parity games requires exponential time

Oliver Friedmann (2012)

RAIRO - Theoretical Informatics and Applications

This paper presents a new lower bound for the recursive algorithm for solving parity games which is induced by the constructive proof of memoryless determinacy by Zielonka. We outline a family of games of linear size on which the algorithm requires exponential time.

Recursive generation of simple planar quadrangulations with vertices of degree 3 and 4

Mahdieh Hasheminezhad, Brendan D. McKay (2010)

Discussiones Mathematicae Graph Theory

We describe how the simple planar quadrangulations with vertices of degree 3 and 4, whose duals are known as octahedrites, can all be obtained from an elementary family of starting graphs by repeatedly applying two expansion operations. This allows for construction of a linear time generator of all graphs in the class with at most a given order, up to isomorphism.

Reducible properties of graphs

P. Mihók, G. Semanišin (1995)

Discussiones Mathematicae Graph Theory

Let L be the set of all hereditary and additive properties of graphs. For P₁, P₂ ∈ L, the reducible property R = P₁∘P₂ is defined as follows: G ∈ R if and only if there is a partition V(G) = V₁∪ V₂ of the vertex set of G such that V G P and V G P . The aim of this paper is to investigate the structure of the reducible properties of graphs with emphasis on the uniqueness of the decomposition of a reducible property into irreducible ones.

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