Even Set Systems

Even Set Systems

In phylogenetic combinatorics, the analysis of split systems is a fundamental issue. Here, we observe that there is a canonical one-to-one correspondence between split systems on the one, and “even” set systems on the other hand, i.e., given any finite set X , we show that there is a canonical one-to-one correspondence between the set P (S(X)) consisting of all subsets S of the set S(X) of all ...

Even Faster Algorithm for Set Splitting!

In the p-Set Splitting problem we are given a universe U , a family F of subsets of U and a positive integer k and the objective is to find a partition of U into W and B such that there are at least k sets in F that have non-empty intersection with both B and W . In this paper we study p-Set Splitting from the view point of kernelization and parameterized algorithms. Given an instance (U,F , k)...

Stability results for set solution of fuzzy integro-differential systems

Projective Models of K3 Surfaces with an Even Set

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a careful analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate the...

Even Triangulations of Planar Set of Points with Steiner Points

Let P ⊂ R be a set of n points of which k are interior points. Let us call a triangulation T of P even if all its vertices have even degree, and pseudo-even if at least the k interior vertices have even degree. (Pseudo-) Even triangulations have one nice property; their vertices can be 3-colored, see [2, 3, 4]. Since one can easily check that for some sets of points, such triangulation do not e...