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, and fit naturally within constraint logic programming. However, in general, filtering that is sound for a global constraint can be unso...

Consider the following relaxation of the Hadwiger Conjecture: For each t there exists Nt such that every graph with no Kt minor admits a vertex partition into dαt + βe parts, such that each component of the subgraph induced by each part has at most Nt vertices. The Hadwiger Conjecture corresponds to the case α = 1, β = −1 and Nt = 1. Kawarabayashi and Mohar [K. Kawarabayashi, B. Mohar, A relaxe...

The problem of the holomorphic contractibility Teichmüller spaces T(0,n) punctured spheres (n>4) arose in 1970s connection with solving algebraic equations Banach algebras. Recently it was solved by author. In present paper, we give a refined proof for all T(0,n), n>4 and provide two independent proofs low-dimensional spaces, which has intrinsic interest.

Graph modification problems such as vertex deletion, edge deletion or edge contractions are a fundamental class of optimization problems. Recently, the parameterized complexity of the contractibility problem has been pursued for various specific classes of graphs. Usually, several graph modification questions of the deletion variety can be seen to be FPT if the graph class we want to delete int...