{We use resonant photoemission spectroscopy (resPES) to study the electronic properties of amorphous ZnO (a-ZnO) layers. We report on the core levels, the valence band (VB) PES data, and the X-ray absorption (XAS) data which we use for the conduction band (CB) density of states. From these results we are able to derive the partial density of states (pDOS) of O2p and Zn4s4p states in the VB and CB, respectively as well as a band scheme. At the O1s resonance we observe a band of localized defect states which is located between the Fermi energy and the CBM. At the Zn2p edge the XAS data indicate that localized Zn4s4p states are involved in the DOS starting already at the Fermi energy. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim}

Given two graphs G and H, an H-decomposition of G is a partition of the
edge set of G such that each part is either a single edge or forms a graph
isomorphic to H. Let f(n;H) be the smallest number  such that any graph
G of order n admits an H-decomposition with at most f(n;H)  parts. Pikhurko and
Sousa conjectured that f(n;H) = ex(n;H) for (H)  3 and all sufficiently
large n, where ex(n;H) denotes the maximum number of edges in a graph on n vertices not containing H as a subgraph. Their conjecture has been veried by
Ozkahya and Person for all edge-critical graphs H. In this article, the conjecture
is veried for the k-fan graph. The k-fan graph, denoted by F_k, is the graph on
2k + 1 vertices consisting of k triangles which intersect in exactly one common
vertex called the centre of the k-fan.