Segment representation of a subclass of co-planar graphs

Details Segment representation of a subclass of co-planar graphs Segment representation of a subclass of co-planar graphs

2010-11-05

arxiv.org/abs/1011.1332v1

Mathematics

Combinatorics

5 pages, 4 figures, preliminary version

Scientific paper

A graph is said to be a segment graph if its vertices can be mapped to line segments in the plane such that two vertices have an edge between them if and only if their corresponding line segments intersect. Kratochv\'{i}l and Kub\v{e}na [``On intersection representations of co-planar graphs'', Discrete Mathematics, 178(1-3):251-255, 1998] asked the question of whether the complements of planar graphs are segment graphs. We show here that the complements of all partial 2-trees are segment graphs.

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