Some new results on circle graphs
نویسنده
چکیده
Abstract: The intersection graph of a set of chords on a circle is called a circle graph. This class of graphs admits some interesting subclasses, such as: Helly circle graphs, clique-Helly circle graphs, unit circle graphs and proper circular-arc graphs. In this paper, we prove some inclusion relations among these subclasses. A necessary condition for a graph being a Helly circle graph is shown and we conjecture that this condition is sufficient too. All possible intersections among these subclasses are analized. The number of regions generated is 10. We show a minimal example belonging to each one of them. Finally, some properties about minimal forbidden subgraphs for circle graphs are proved.
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