Conflict-Free Coloring of Intersection Graphs
نویسندگان
چکیده
منابع مشابه
Conflict-Free Coloring of Intersection Graphs
A conflict-free k-coloring of a graph G = (V,E) assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and v’s neighbors. Such colorings have applications in wireless networking, robotics, and geometry, and are well studied in graph theory. Here we study the conflictfree coloring of geometric inter...
متن کاملConflict-free coloring of graphs
We study the conflict-free chromatic number χCF of graphs from extremal and probabilistic point of view. We resolve a question of Pach and Tardos about the maximum conflict-free chromatic number an n-vertex graph can have. Our construction is randomized. In relation to this we study the evolution of the conflict-free chromatic number of the ErdősRényi random graph G(n, p) and give the asymptoti...
متن کاملThree Colors Suffice: Conflict-Free Coloring of Planar Graphs
A conflict-free k-coloring of a graph assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and v’s neighbors. Such colorings have applications in wireless networking, robotics, and geometry, and are well-studied in graph theory. Here we study the natural problem of the conflict-free chromatic num...
متن کاملConflict-Free Coloring Made Stronger
In FOCS 2002, Even et al. showed that any set of n discs in the plane can be Conflict-Free colored with a total of at most O(log n) colors. That is, it can be colored with O(log n) colors such that for any (covered) point p there is some disc whose color is distinct from all other colors of discs containing p. They also showed that this bound is asymptotically tight. In this paper we prove the ...
متن کاملOn Conflict-Free Multi-coloring
A conflict-free coloring of a hypergraph H = (V, E), E ⊆ 2 , is a coloring of the vertices V such that every hyperedge E ∈ E contains a vertex of “unique” color. Our goal is to minimize the total number of distinct colors. In its full generality, this problem is known as the conflictfree (hypergraph) coloring problem. It is known that Θ( √ m) colors might be needed in general. In this paper we ...
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ژورنال
عنوان ژورنال: International Journal of Computational Geometry & Applications
سال: 2018
ISSN: 0218-1959,1793-6357
DOI: 10.1142/s0218195918500085