Divergences in QED on a Graph

We consider a model of quantum electrodynamics (QED) on a graph. The one-loop divergences in the model are investigated by use of the background field method.Comment: 14 pages, no figures, RevTeX4. References and typos adde

Bug propagation and debugging in asymmetric software structures

Software dependence networks are shown to be scale-free and asymmetric. We then study how software components are affected by the failure of one of them, and the inverse problem of locating the faulty component. Software at all levels is fragile with respect to the failure of a random single component. Locating a faulty component is easy if the failures only affect their nearest neighbors, while it is hard if the failures propagate further.Comment: 4 pages, 4 figure

Embedding cycles of given length in oriented graphs

Kelly, Kuehn and Osthus conjectured that for any l>3 and the smallest number k>2 that does not divide l, any large enough oriented graph G with minimum indegree and minimum outdegree at least \lfloor |V(G)|/k\rfloor +1 contains a directed cycle of length l. We prove this conjecture asymptotically for the case when l is large enough compared to k and k>6. The case when k<7 was already settled asymptotically by Kelly, Kuehn and Osthus.Comment: 8 pages, 2 figure

RÓZSA (ROSA )PÉTER

As her adoptive son, I shared a flat with Rózsa Péter for almost a quarter of a century, so I could recount very much about Professor Peter, about "Aunt Rosa" to so many. However, the chronicler will hardly be able to give a full picture, on a few short pages, of the significance in education and scientific progress of her generous activities stemming from love of humanity and of science. The two dates on her sepulchral monument erected by the Hungarian Academy of Sciences are: 1905-1977

On the connection between chromatic number, maximal clique and minimal degree of a graph

Abstract. Let G n be a graph of n vertices, having chromatic number r which contains no complete graph of r vertices. Then G n contains a vertex of degree not exceeding n(3r-7)í(3r-4). The result is essentially best possible. In this paper we shall use the following notations: Gn denotes a graph of n vertices, without loops and multiple edges; V(G n) respectively E(G, ) the set of vertices respectively the set of edges of G,