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The Tutte polynomial of a graph, depth-first search, and simplicial complex partitions
The electronic journal of combinatorics, The Foata Festschrift volume, Tome 3 (1996) no. 2
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One of the most important numerical quantities that can be computed from a graph $G$ is the two-variable Tutte polynomial. Specializations of the Tutte polynomial count various objects associated with $G$, e.g., subgraphs, spanning trees, acyclic orientations, inversions and parking functions. We show that by partitioning certain simplicial complexes related to $G$ into intervals, one can provide combinatorial demonstrations of these results. One of the primary tools for providing such a partition is depth-first search.
DOI : 10.37236/1267
Classification : 05C30, 05C05, 68R10
Mots-clés : Tutte polynomial, simplicial complexes, partition, depth-first search 
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     author = {Ira M. Gessel and Bruce E. Sagan},
     title = {The {Tutte} polynomial of a graph, depth-first search, and simplicial complex partitions},
     journal = {The electronic journal of combinatorics},
     year = {1996},
     volume = {3},
     number = {2},
     doi = {10.37236/1267},
     zbl = {0857.05046},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1267/}
}
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Ira M. Gessel; Bruce E. Sagan. The Tutte polynomial of a graph, depth-first search, and simplicial complex partitions. The electronic journal of combinatorics, The Foata Festschrift volume, Tome 3 (1996) no. 2. doi: 10.37236/1267

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