Fourientation activities and the Tutte polynomial

A fourientation of a graph G is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. We may naturally view fourientations as a mixture of subgraphs and graph orientations where unoriented and bioriented edges play the role of absent and present subgraph edges, respectively. Building on work of Backman and Hopkins (forthcoming), we show that given a linear order and a reference orientation of the edge set, one can define activities for fourientations of G which allow for a new 12 variable expansion of the Tutte polynomial T-G. Our formula specializes to both an orientation activities expansion of T-G due to Las Vergnas (1984) and a generalized activities expansion of T-G due to Gordon and Traldi (1990).

Title	Fourientation activities and the Tutte polynomial
Creator	Backman, S.
	Hopkins, S.
	Traldi, Lorenzo
Publisher	European Journal of Combinatorics
Academic Department	Mathematics
Division	Natural Sciences
Organization	Lafayette College
Date Issued	January 2018
Date Available	2020-01-02
Type	Article
Language	English
Bibliographic Citation	Backman, S., S. Hopkins, and L. Traldi (2018 Jan) "Fourientation activities and the Tutte polynomial." European Journal of Combinatorics 67: 40-60.
Standard Identifier	Handle 10385/tt44pn30j
Standard Identifier	DOI 10.1016/j.ejc.2017.07.002
Permalink	http://hdl.handle.net/10385/tt44pn30j
Rights Statement	In Copyright
Rights Holders	Elsevier Ltd.