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Abstract

The two diagrams in Figure 8.1 represent the same graph, a K 4 with vertices a, b, c and d. As diagrams they are quite different: in the left-hand version, the edges ac and bd cross; in the right-hand version there are no crossings. We shall refer to the two diagrams as different representations of the graph in the plane. The crossing number of a representation is the number of different pairs of edges that cross; the crossing number v(G) of a graph G is the minimum number of crossings in any representation of G. A representation is called planar if it contains no crossings, and a planar graph is a graph that has a planar representation. In other words, a planar graph G is one for which v(G) = 0. Figure 8.1 shows that v(K 4) = 0.

Keywords

Planar Graph Exchange Color Complete Bipartite Graph Plane Representation Petersen Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • W. D. Wallis
    • 1
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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