On some subclasses of circular-arc graphs
نویسندگان
چکیده
The intersection graph of a family of arcs on a circle is called a circular-arc graph. This class of graphs admits some interesting subclasses: proper circular-arc graphs, unit circular-arc graphs, Helly circular-arc graphs and clique-Helly circular-arc graphs. In this paper, all possible intersections of these subclasses are studied. There are thirteen regions. Twelve of these are nonempty, and we construct a minimal graph in each of them. Our main result is that the thirteenth region is empty, namely we prove that among proper but no unit circular-arc graphs, every clique-Helly circular-arc graph is also a Helly circular-arc graph.
منابع مشابه
The intersection between some subclasses of circular-arc and circle graphs
The intersection graph of a family of arcs on a circle is called a circular-arc graph. This class of graphs admits some interesting subclasses: proper circular-arc graphs, unit circular-arc graphs, Helly circular-arc graphs and clique-Helly circular-arc graphs. The intersection graph of a family of chords in a circle is called a circle graph. Analogously, this class of graphs admits some subcla...
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