Rhombic embeddings of planar graphs with faces of degree 4

Given a finite or infinite planar graph all of whose faces have degree 4, we study embeddings in the plane in which all edges have length 1, that is, in which every face is a rhombus. We give a necessary and sufficient condition for the existence of such an embedding, as well as a description of the set of all such embeddings.Comment: 11 pages, 3 figure

Top quark in theory

I review how the top quark is embedded in the Standard Model and some its proposed extensions, and how it manifests itself in various hadron collider signals.Comment: 12 page

Top-BESS model and its phenomenology

We introduce the top-BESS model which is the effective description of the strong electroweak symmetry breaking with a single new SU(2)_L+R triplet vector resonance. The model is a modification of the BESS model in the fermion sector. The triplet couples to the third generation of quarks only. This approach reflects a possible extraordinary role of the top quark in the mechanism of electroweak symmetry breaking. The low-energy limits on the model parameters found provide hope for finding sizable signals in the LHC Drell-Yan processes as well as in the s-channel production processes at the ILC. However, there are regions of the model parameter space where the interplay of the direct and indirect fermion couplings can hide the resonance peak in a scattering process even though the resonance exists and couples directly to top and bottom quarks.Comment: published in Physical Review D, minor changes in text, 21 pages, 37 figure

On the approximability of the maximum induced matching problem

In this paper we consider the approximability of the maximum induced matching problem (MIM). We give an approximation algorithm with asymptotic performance ratio <i>d</i>-1 for MIM in <i>d</i>-regular graphs, for each <i>d</i>≥3. We also prove that MIM is APX-complete in <i>d</i>-regular graphs, for each <i>d</i>≥3