{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:18:07Z","timestamp":1759335487465,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.37236\/1267","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:52:04Z","timestamp":1578707524000},"source":"Crossref","is-referenced-by-count":20,"title":["The Tutte Polynomial of a Graph, Depth-first Search"],"prefix":"10.37236","volume":"3","author":[{"given":"Ira M.","family":"Gessel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruce E.","family":"Sagan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[1995,6,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i2r9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i2r9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T09:31:42Z","timestamp":1579339902000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i2r9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,6,14]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[1996,1,24]]}},"URL":"https:\/\/doi.org\/10.37236\/1267","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1995,6,14]]},"article-number":"R9"}}