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An extension of the basic image reconstruction problem in discrete tomography is considered: given a graph G=(V,E) and a family P of chains Pi together with vectors h(Pi)=(hi1,...,hik), one wants to find a partition $V^{1},. ...
We show that every graph G with maximum degree three has a straight-line drawing in the plane using edges of at most five different slopes. Moreover, if G is connected and has at least one vertex of degree less than three, then four directions suffice. ...
A goal of this paper is to efficiently adapt the best ingredients of the graph colouring techniques to an NP-hard satellite range scheduling problem, called MuRRSP. We propose two new heuristics for the MuRRSP, where as many jobs as possible have to be sch ...
We are interested in coloring the vertices of a mixed graph, i.e., a graph containing edges and arcs. We consider two different coloring problems: in the first one we want adjacent vertices to have different colors and the tail of an arc to get a color str ...
We consider the coloring problem for mixed graphs, that is, for graphs containing edges and arcs. A mixed coloring c is a coloring such that for every edge [xi,xj], c(xi)=c(xj) and for every arc (xp,xq), $c(x_{p})
Let G = (V, E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1, ..., k}) to each vertex of G so that no edge has both endpoints with the same color. We propose a new local search methodology, ...
In this note we consider two coloring problems in mixed graphs, i.e., graphs containing edges and arcs. We show that they are both NP-complete in cubic planar bipartite graphs. This answers an open question from \cite{Ries2}. ...
We study online partitioning of posets from a graph theoretical point of view, which is coloring and cocoloring in comparability graphs. For the coloring problem, we analyse the First-Fit algorithm and show a ratio of O(n); furthermore, we devise ...
We consider the problem of finding in a graph a set R of edges to be colored in red so that there are maximum matchings having some prescribed numbers of red edges. For regular bipartite graphs with n nodes on each side, we give sufficient conditions f ...
The graph coloring problem is one of the most famous problems in graph theory and has a large range of applications. It consists in coloring the vertices of an undirected graph with a given number of colors such that two adjacent vertices get different col ...
