Determinantal generating functions of colored spanning forests
The color type of a spanning forest of a graph with colored edges is defined and, subsequently, it is proved that the generating function of such spanning forests is obtained as the formal expansion of a certain determinant. An analogous determinantal expansion yields the generating function of all...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204302206 |
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| Summary: | The color type of a spanning forest of a graph with colored edges
is defined and, subsequently, it is proved that the generating function of such spanning forests is obtained as the formal expansion of a certain determinant. An analogous determinantal expansion yields the generating function of all spanning forests
of a given color type that contain a specific subforest. Algorithms are described for obtaining a list of all colored spanning trees and spanning forests of any graph with colored edges based on symbolic calculation. |
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| ISSN: | 0161-1712 1687-0425 |