Consecutive patterns: from permutations to column-convex polyominoes and back.
A constrained colouring or, more specifically, an (α, β)-colouring of a hypergraph H, is an assignment of colours to its vertices such that no edge of H contains less than α or more than β vertices with different colours. This notion, introduced by Bujtás and Tuza, generalises both classical hypergraph colourings and more general Voloshin colourings of hypergraphs. In fact, for r-uniform hypergraphs, classical colourings correspond to (2, r)-colourings while an important instance of Voloshin colourings...
In this paper, we study the problem of computing a minimum cost Steiner tree subject to a weight constraint in a Halin graph where each edge has a nonnegative integer cost and a nonnegative integer weight. We prove the NP-hardness of this problem and present a fully polynomial time approximation scheme for this NP-hard problem.
In this paper, we study the problem of computing a minimum cost Steiner tree subject to a weight constraint in a Halin graph where each edge has a nonnegative integer cost and a nonnegative integer weight. We prove the NP-hardness of this problem and present a fully polynomial time approximation scheme for this NP-hard problem.
Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.The author developed computer programs needed for the classification of designs with certain automorphisms by the local approach method. All these programs use canonicity test or/and construction of canonical form of an integer matrix. Their efficiency substantially influences the speed of the whole computation. The present paper deals with the implemented canonicity algorithm. It is based on ideas used by McKay, Meringer,...
We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of mutually orthogonal Latin squares of order to construct a set of mutually orthogonal Latin squares of order .
The number of -gaussoids is shown to be a double exponential function in . The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing -minors and encoding the resulting combinatorial constraints in a suitable transitive graph. Various special classes of gaussoids arise from restricting the allowed -minors.