1. Right angle crossing graphs and 1-planarity
- Author
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Eades, Peter and Liotta, Giuseppe
- Subjects
- *
PLANAR graphs , *GRAPH theory , *COMBINATORICS , *INTERSECTION theory , *PROOF theory , *ALGEBRAIC geometry - Abstract
Abstract: A Right Angle Crossing Graph (also called a RAC graph for short) is a graph that has a straight-line drawing where any two crossing edges are orthogonal to each other. A -planar graph is a graph that has a drawing where every edge is crossed at most once. This paper studies the combinatorial relationship between the family of RAC graphs and the family of -planar graphs. It is proved that: (1) all RAC graphs having maximal edge density belong to the intersection of the two families; and (2) there is no inclusion relationship between the two families. As a by-product of the proof technique, it is also shown that every RAC graph with maximal edge density is the union of two maximal planar graphs. [Copyright &y& Elsevier]
- Published
- 2013
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