Journal of Mathematical Sciences

, Volume 209, Issue 6, pp 809–825 | Cite as

Chip Removal. Urban Renewal Revisited


We describe a new combinatorial-algebraic transformation on graphs which we call the “chip removal.” It generalizes the well-known urban renewal trick of Propp and Kuperberg. The chip removal is useful in calculations of the determinants of adjacency matrices and matching numbers of graphs. A beautiful example of applying this technique is a theorem on removing 4-contact chips, which generalizes Kuo’s graphical condensation method. Numerous examples are given. Bibliography: 6 titles.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.ITMO UniversitySt.PetersburgRussia

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