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Journal of Mathematical Sciences

, Volume 215, Issue 6, pp 631–648 | Cite as

Calculation of Pfaffians by a Chip Removal

  • V. E. Aksenov
  • K. P. Kokhas
Article
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We describe a new combinatorial-algebraic transformation on graphs which we call “chip removal.” It generalizes the well-known Urban Renewal trick of Propp and Kuperberg. The chip removal is useful in calculations of determinants of adjacency matrices and matching numbers of graphs. A beautiful example of this technique is a theorem on removing four-contact chips, which generalizes Kuo’s graphical condensation method. Numerous examples are given. Bibliography: 10 titles.

Keywords

White Vertex External Edge Matching Number Chip Removal External Vertex 
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 2016

Authors and Affiliations

  1. 1.ITMO UniversitySt. PetersburgRussia
  2. 2.St.Petersburg State UniversitySt. PetersburgRussia

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