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The Incidence Hopf Algebra of Graphs
dc.contributor.author | Humpert, Brandon Eugene | |
dc.contributor.author | Martin, Jeremy L. | |
dc.date.accessioned | 2015-03-05T17:17:46Z | |
dc.date.available | 2015-03-05T17:17:46Z | |
dc.date.issued | 2012-05-03 | |
dc.identifier.citation | Humpert, Brandon & Martin, Jeremy L. "The Incidence Hopf Algebra of Graphs." (2012) SIAM J. Discrete Math., 26(2), 555–570. (16 pages). http://dx.doi.org/10.1137/110820075. | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/16971 | |
dc.description | This is the published version, also available here: http://dx.doi.org/10.1137/110820075. | en_US |
dc.description.abstract | The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf algebra, whose basis elements correspond to finite graphs, and whose Hopf product and coproduct admit simple combinatorial descriptions. We give a new formula for the antipode in the graph algebra in terms of acyclic orientations; our formula contains many fewer terms than Takeuchi's and Schmitt's more general formulas for the antipode in an incidence Hopf algebra. Applications include several formulas (some old and some new) for evaluations of the Tutte polynomial. | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.subject | combinatiorial Hopf algebra | en_US |
dc.subject | graph | en_US |
dc.subject | chromatic polynomial | en_US |
dc.subject | tutte polynomial | en_US |
dc.subject | acyclic orientation | en_US |
dc.title | The Incidence Hopf Algebra of Graphs | en_US |
dc.type | Article | |
kusw.kuauthor | Martin, Jeremy L. | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.1137/110820075 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item meets KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess |