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The Tutte decomposition

  • W. T. Tutte
  • Curtis Greene
  • Thomas Zaslavsky

Abstract

“Simple ideas are often the most powerful.” This adage is best exemplified in matroid theory by the method of Tutte (-Grothendieck) decomposition. This method has its origin in the following recursion formula (due to Foster1); see the concluding note in Whitney [32]) for the chromatic polynomial P(L; λ) of a graph L. Let L be a graph and A an edge in L linking two distinct vertices. Let L A be the graph obtained from L by deleting the edge A and L A the graph obtained from L by contracting A. Then
$$P(L;{\mkern 1mu} \lambda ){\mkern 1mu} = {\mkern 1mu} P({L'_A};{\mkern 1mu} \lambda ){\mkern 1mu} - {\mkern 1mu} P({L''_A};{\mkern 1mu} \lambda ).$$

Keywords

Isomorphism Class Linear Code Critical Problem Simple Closed Curve Linear 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 1986

Authors and Affiliations

  • W. T. Tutte
    • 1
  • Curtis Greene
    • 2
  • Thomas Zaslavsky
  1. 1.Trinity CollegeCambridgeUSA
  2. 2.Massachusetts Institute of TechnologyUSA

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