Zariski decompositions of numerical cycle classes

Restricted Volumes and Divisorial Zariski Decompositions

We give a relation between the existence of a Zariski decomposition and the behavior of the restricted volume of a big divisor on a smooth (complex) projective variety. Moreover, we give an analytic description of the restricted volume in the line of Boucksom’s work. It enables us to define the restricted volume of a transcendental class on a compact Kähler manifold in natural way. The relation...

5-cycle Decompositions from Paired 3- and 4-cycle Decompositions

Let (V, T ) be a 3-fold triple system and (V,C) a 4-fold 4-cycle system on the same set V . This choice of indices 3 and 4 ensures that each system contains the same number of cycles: |T | = |C|. We pair up the cycles, {t, c}, where t ∈ T and c ∈ C, in such a way that t and c share one edge. If t = (x, y, z) and c = (x, y, u, v), so t and c share the edge {x, y}, then we retain the 5-cycle (z, ...

Path And Cycle Decompositions

First I want to say a few words about my graph terminology. If I want to allow loops, I use the adjective reflexive. If I want to allow multiple edges, I use multigraph. Thus, a graph has no loops and no multiple edges. I use valency rather than degree. If we say a graph is 4-valent (or tetravalent), it means it is regular of valency 4, for example. A decomposition of a graph X is a partition o...

Trend-Cycle Decompositions

4-Cycle Decompositions of Graphs

In this paper we consider the problem of finding the smallest number  such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most  elements. We solve this problem for n sufficiently large.