On-line coloring of geometric intersection graphs
نویسندگان
چکیده
منابع مشابه
On-Line Approach to Off-Line Coloring Problems on Graphs with Geometric Representations
The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs with geometric representations and competitive analysis of on-line algorithms, which became apparent after the recent construction of triangle-free geometric intersection graphs with arbitrarily large chromatic number due to Pawlik et al. We show that on-line graph coloring problems give ...
متن کاملGeometric Intersection Graphs: Problems and Directions Collection of Open Problems 1. Coloring segment intersection graphs avoiding monochromatic cliques Proposer:
For a graph G and an integer k ≥ 2, let χk(G) denote the minimum number of colors in a coloring of the vertices of G such that no k-clique of G is monochromatic. In particular, χ2(G) is the ordinary chromatic number of G. It is known that triangle-free segment intersection graphs can have arbitrarily large chromatic number. It is also known that Kk-free string graphs can have arbitrarily large ...
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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 کاملTractabilities and Intractabilities on Geometric Intersection Graphs
A graph is said to be an intersection graph if there is a set of objects such that each vertex corresponds to an object and two vertices are adjacent if and only if the corresponding objects have a nonempty intersection. There are several natural graph classes that have geometric intersection representations. The geometric representations sometimes help to prove tractability/intractability of p...
متن کاملBidimensionality of Geometric Intersection Graphs
Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric intersection graphs GB where each body of the collection B is represented by a vertex, and two vertices of GB are adjacent if the intersection of the correspon...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2002
ISSN: 0925-7721
DOI: 10.1016/s0925-7721(02)00089-5