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Graph theory is an important topic in discrete mathematics. It is particularly interesting because it has a wide range of applications. Among the main problems in graph theory, we shall mention the following ones: graph coloring and the Hamiltonian circuit ...
The interference graph for a procedure in Static Single Assignment (SSA) Form is chordal. Since the k-colorability problem can be solved in polynomial-time for chordal graphs, this result has generated interest in SSA-based heuristics for spilling and coal ...
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})
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 ...
A colouring of the vertices of a hypergraph H is called conflict-free if each hyperedge E of H contains a vertex of 'unique' colour that does not get repeated in E. The smallest number of colours required for such a colouring is called the conflict-free ch ...
Most of the recent heuristics for the graph coloring problem start from an infeasible k-coloring (adjacent vertices may have the same color) and try to make the solution feasible through a sequence of color exchanges. In contrast, our approach (called FOO- ...
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 ...
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},. ...
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, ...
