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We study complexity and approximation of MIN WEIGHTED NODE COLORING in planar, bipartite and split graphs. We show that this problem is NP-hard in planar graphs, even if they are triangle-free and their maximum degree is bounded above by 4. Then, we prove ...
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 grap ...
Extensions and variations of the basic problem of graph coloring are introduced. The problem consists essentially in finding in a graph G a k-coloring, i.e., a partition V-1,...,V-k of the vertex set of G such that, for some specified neighborhood (N) over ...
Starting from the basic problem of reconstructing a 2-dimensional image given by its projections on two axes, one associates a model of edge coloring in a complete bipartite graph. The complexity of the case with k=3 colors is open. Variations and special ...
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 ...
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 ...
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}. ...
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},. ...
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- ...
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 ...
