A Programmer's Guide to Computer Science: A virtual degree for the self-taught developer by William Springer
Author:William Springer [Springer, William]
Language: eng
Format: epub
Publisher: Jaxson Media
Published: 2019-08-09T22:00:00+00:00
Chapter 7: Common Graph Classes
Many problems are quite difficult (NP-hard) on arbitrary graphs, but have efficient (or even trivial) solutions on graphs in a particular class. Inversely, a problem may be known to have no solution on graphs of a particular class. Thus, we can often save ourselves a great deal of trouble if we can demonstrate that a problem instance belongs to a particular class of graphs.
7.1 Forbidden subgraphs
A forbidden subgraph characterization of a class of graphs defines a set of structures that may not appear in the graph; the presence or absence of these structures determines whether or not the graph belongs to the class. These forbidden substructures can be defined in a number of ways:
Graphs
A graph may belong to a class only if it does not contain any subgraph from a (possibly infinite) set. For example, the bipartite graphs are exactly those which contain no odd cycles.
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