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Topology
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Abstract
The primary focus of this chapter involves putting graphs on surfaces. Questions that we discuss include the following. Which graphs are planar; that is, which graphs can be drawn in the plane without any edges crossing? If a graph is not planar, what is the smallest number of crossings in any drawing of it? How many planar graphs are needed to form a given graph? In what surfaces can a non-planar graph be embedded? There are many links between graph theory and topology, but the strongest is that of drawings and embeddings of graphs on surfaces. Our survey of this area of mathematics is divided into two parts, the first (Sections 11.2-11.4) on graphs in the plane, including the topics of crossing number and thickness, and the second (Sections 11.5-11.8) on embeddings in other surfaces, both orientable and non-orientable.
Title: Topology
Description:
Abstract
The primary focus of this chapter involves putting graphs on surfaces.
Questions that we discuss include the following.
Which graphs are planar; that is, which graphs can be drawn in the plane without any edges crossing? If a graph is not planar, what is the smallest number of crossings in any drawing of it? How many planar graphs are needed to form a given graph? In what surfaces can a non-planar graph be embedded? There are many links between graph theory and topology, but the strongest is that of drawings and embeddings of graphs on surfaces.
Our survey of this area of mathematics is divided into two parts, the first (Sections 11.
2-11.
4) on graphs in the plane, including the topics of crossing number and thickness, and the second (Sections 11.
5-11.
8) on embeddings in other surfaces, both orientable and non-orientable.
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