Regular spanning subgraphs of bipartite graphs of high minimum degree

Let G be a simple balanced bipartite graph on $2n$ vertices, $\delta = \delta(G)/n$, and $\rho={\delta + \sqrt{2 \delta -1} \over 2}$. If $\delta > 1/2$ then it has a $\lfloor \rho n \rfloor$-regular spanning subgraph. The statement is nearly tight.Comment: submitte

On embedding well-separable graphs

Call a simple graph $H$ of order $n$ well-separable, if by deleting a separator set of size $o(n)$ the leftover will have components of size at most $o(n)$. We prove, that bounded degree well-separable spanning subgraphs are easy to embed: for every $\gamma >0$ and positive integer $\Delta$ there exists an $n_0$ such that if $n>n_0$, $\Delta(H) \le \Delta$ for a well-separable graph $H$ of order $n$ and $\delta(G) \ge (1-{1 \over 2(\chi(H)-1)} + \gamma)n$ for a simple graph $G$ of order $n$, then $H \subset G$. We extend our result to graphs with small band-width, too.Comment: 11 pages, submitted for publicatio

Embedding graphs having Ore-degree at most five

Let $H$ and $G$ be graphs on $n$ vertices, where $n$ is sufficiently large. We prove that if $H$ has Ore-degree at most 5 and $G$ has minimum degree at least $2n/3$ then $H\subset G.$Comment: accepted for publication at SIAM J. Disc. Mat

Optimal Random Matchings, Tours, and Spanning Trees in Hierarchically Separated Trees

We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size $n$ distributed among the leaves of a balanced hierarchically separated tree. We consider {\it monochromatic} and {\it bichromatic} versions of the minimum matching, minimum spanning tree, and traveling salesman problems. We also present tight concentration results for the monochromatic problems.Comment: 24 pages, to appear in TC

EXPERIMENTAL EXAMINATIONS OF THE LOGISTICS PARAMETERS OF AN INDUCTIVE RADIO FREQUENCY IDENTIFICATION SYSTEMS

There are two main factors determining the applicability of an inductive radio frequency identification (RFID) system for dynamic operations: the logistics parameters (communication range, amount of transmittable data, communication time and speed of data carrier) and their effects on each other. The aim of the research of the Department of Building and Material Handling Machines, Technical University of Budapest, in cooperation with OMRON Electronics Hungary Ltd., is to develop a new measuring and analysing method to examine the logistics parameters mentioned above and to simulate their effects on each other. This method helps the end-users to choose the proper RFID system to be used in a given application, where RFID system will operate in dynamic conditions and the material-flow requires a lot of constantly changing information. This study gives a description of the research, its main steps, the executed examinations and their results. Furthermore, it indicates what additional tasks have to be executed to accomplish the research