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In a graph , contraction of an edge with endpoints is the replacement of and with a single vertex such that edges incident to the new vertex are the edges other than that were incident with or . The resulting graph, denoted , has one less edge than .
Graph minors are defined in terms of edge contractions.
Bollobás, B. Modern Graph Theory. New York: Springer-Verlag, 1998.Diestel, R. Graph Theory, 3rd ed. New York: Springer-Verlag, 1997.
West, D. B. Introduction to Graph Theory, 2nd ed. Upper Saddle River, NJ: Prentice Hall, p. 84, 2001.
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