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

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.


White Vertex External Edge Matching Number Chip Removal External Vertex 
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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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