On the structure of certain intersection graphs

Authors:
Kathie Cameron;Chính T. Hoàng
Affiliations:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada;Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada
Venue:
Information Processing Letters
Year:
2006

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Abstract

Recently Gavril introduced a new class of intersection graphs called interval-filament graphs. These include co-comparability graphs and polygon-circle graphs (the intersection graphs of polygons inscribed in a circle), which include circular-arc graphs (the intersection graphs of arcs of a circle), circle graphs (the intersection graphs of chords of a circle), chordal graphs, and outerplanar graphs. We give a structural property of polygon-circle graphs. We prove a bound on the clique-covering number for interval-filament graphs in terms of the size of a largest independent set of nodes in the graph. We prove that complements of interval-filament graphs are 4-divisible in the sense of Hoàng and McDiarmid. Similar results are obtained for complements of other intersection graphs introduced by Gavril.