Covering and coloring polygon-circle graphs

Covering and coloring polygon-circle graphs

Polygon-circle graphs are intersection graphs of polygons inscribed in a circle. This class of graphs includes circle graphs (intersection graphs of chords of a circle), circular arc graphs (intersection graphs of arcs on a circle), chordal graphs and outerplanar graphs. We investigate binding functions for chromatic number and clique covering number of polygon-circle graphs in terms of their c...

On polygon numbers of circle graphs and distance hereditary graphs

Circle graphs are intersection graphs of chords in a circle and kpolygon graphs are the intersection graphs of chords in a convex ksided polygon where each chord has its endpoints on distinct sides. Every k-polygon graph is a circle graph and every circle graph is a kpolygon graph for some k. The polygon number ψ(G) of a circle graph G is the minimum k such that G is a k-polygon graph and the p...

Coloring Clean and K4-free Circle Graphs

A circle graph is the intersection graph of chords drawn in a circle. The best known general upper bound on the chromatic number of circle graphs with clique number k is 50 · 2. We prove a stronger bound of 2k − 1 for graphs in a simpler subclass of circle graphs, so called clean graphs. Based on this result we prove that the chromatic number of every circle graph with clique number at most 3 i...

Polygon Generalization with Circle Arcs

Despite the current high capacity and speed of computers, the efficient storage of spatial data is still a cutting edge issue, most notably in the context of mobile devices. Processing power, limited storage and small display on mobile devices all mean that algorithms which efficiently summarize spatial data, reducing its size, have relevance. Generalization also has an important role to play i...

Covering on a Circle