Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible component of subgame perfect equilibria. Finally, the graph of the subgame perfect equilibrium correspo...

Open forms of global constraints allow the addition of new variables to an argument during the execution of a constraint program. Such forms are needed for difficult constraint programming problems where problem construction and problem solving are interleaved. However, in general, filtering that is sound for a global constraint can be unsound when the constraint is open. This paper provides a ...

Let X be a smooth, complete toric variety. Let A1(X) be the group of algebraic 1-cycles on X modulo numerical equivalence and N1(X) = A1(X) ⊗Z Q . Consider in N1(X) the cone NE(X) generated by classes of curves on X. It is a well-known result due to M. Reid [11] that NE(X) is closed, polyhedral and generated by classes of invariant curves on X. The variety X is projective if and only if NE(X) i...

We prove a discrete Jordan-Brouwer-Schoenflies separation theorem telling that a (d − 1)-sphere H embedded in a d-sphere G defines two different connected graphs A,B in G such a way that A ∩B = H and A ∪B = G and such that the complementary graphs A,B are both d-balls. The graph theoretic definitions are due to Evako: the unit sphere of a vertex x of a graph G = (V,E) is the graph generated by ...