The aim of the present paper is to show how a slight generalization of a splitting-off result of Berstimas and Teo [1] offers a common understanding of several seemingly unrelated results in graph connectivity theory.

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with electron and muon vacuum polarizations. We calculate single-logarithmic and nonlogarithmic contributions of order alpha;{3}(m/M)E_{F} generated by gauge invariant sets of diagrams with electron and muon polarization insertions in the electron and muon factors. Combining these cor...

In this paper we propose a new combinatorial technique for obtaining data dependent generalization bounds. We introduce a splitting and connectivity graph (SC-graph) over the set of classifiers. In some cases the knowledge of this graph leads to an exact generalization bound. Typically, the knowledge of a little part of the SC-graph is sufficient for reasonable approximation of the bound. Being...

This paper extends the Birkhoff-von Neumann unicast switching strategy to the multicast case. Using a graph theoretic model we show that the rate region for a traffic pattern is precisely the stable set polytope of the pattern’s ‘conflict graph’, in the no-fanout splitting case. Computing the offline schedule is equivalent to fractional weighted graph coloring which takes polynomial time for pe...

Any closed orientable and smooth non-positively curved manifold M is known to admit a geometric characteristic splitting, analogous to the JSJ decomposition in three dimensions. We show that when this splitting consists of pieces which are Seifert fibered or pieces each of whose fundamental group has non-trivial centre, M collapses with bounded curvature and has zero Perelman invariant.