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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