33 search results - page 1 / 7 » On the Chromatic Number of Intersection Graphs of Convex Set... |
COMBINATORICS
2004
13 years 4 months ago
2004
Let G be the intersection graph of a finite family of convex sets obtained by translations of a fixed convex set in the plane. We show that every such graph with clique number k i...
DAM
2006
13 years 4 months ago
2006
To a set of n points in the plane, one can associate a graph that has less than n2 vertices and has the property that k-cliques in the graph correspond vertex sets of convex k-gon...
CORR
2010
Springer
13 years 4 months ago
2010
Springer
We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of fini...
JGT
2008
13 years 4 months ago
2008
Let C be a family of n compact connected sets in the plane, whose intersection graph G(C) has no complete bipartite subgraph with k vertices in each of its classes. Then G(C) has ...
CORR
2008
Springer
13 years 4 months ago
2008
Springer
Map vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least a unit distance apart. The plane-width of a graph is th...