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Graph theory experienced a remarkable increase of interest among the scientific community during the last decades. The vertex coloring problem (Min Coloring) deserves a particular attention rince it has been able to capture a wide variety of applications. ...
Parity (matching theory) and connectivity (network flows) are two main branches of combinatorial optimization. In an attempt to understand better their interrelation, we study a problem where both parity and connectivity requirements are imposed. The main ...
Network tomography infers internal network characteristics by sending and collecting probe packets from the network edge. Traditional tomographic techniques for general topologies typically use a mesh of multicast trees and/or unicast paths to cover the en ...
Assembling partial views is an attractive means to extend the field of view of microscope images. In this paper, we propose a semi-automated solution to achieve this goal. Its intended audience is the microscopist who desires to scan a large area while acq ...
Graph Coloring is a very active field of research in graph theory as well as in the domain of the design of efficient heuristics to solve problems which, due to their computational complexity, cannot be solved exactly (no guarantee that an optimal solution ...
Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s,k)-polar if there exists a partition A,B of its vertex set such that A induces a complete s-partite graph ...
We consider vertex k-colorings of an arbitrary simple, connected, and undirected graph G=(V,E) such that, for every vertex v, at most lambda different colors occur in the closed neighborhood of v. These colorings are called (k,lambda)-colorings. If a graph ...
We consider the problem of partitioning the node set of a graph into p cliques and k stable sets, namely the (p,k)-coloring problem. Results have been obtained for general graphs \cite{hellcomp}, chordal graphs \cite{hellchordal} and cacti for the case whe ...
The common point between the different chapters of the present work is graph theory. We investigate some well known graph theory problems, and some which arise from more specific applications. In the first chapter, we deal with the maximum stable set probl ...
We consider a multicast configuration with two sources, and translate the network code design problem to vertex coloring of an appropriately defined graph. This observation enables to derive code design algorithms and alphabet size bounds, as well as estab ...
