Editing Hamiltonian path (section)

== The Hamiltonian cycle polynomial ==

An algebraic representation of the Hamiltonian cycles of a given weighted digraph (whose arcs are assigned weights from a certain ground field) is the [[Hamiltonian cycle polynomial]] of its weighted adjacency matrix defined as the sum of the products of the arc weights of the digraph's Hamiltonian cycles. This polynomial is not identically zero as a function in the arc weights if and only if the digraph is Hamiltonian. The relationship between the computational complexities of computing it and [[computing the permanent]] was shown by Grigoriy Kogan.<ref>{{Cite book| first = Grigoriy |last = Kogan
 |title = Proceedings of 37th Conference on Foundations of Computer Science
 |chapter = Computing permanents over fields of characteristic 3: Where and why it becomes difficult
 |pages = 108–114
 | year = 1996
 |doi = 10.1109/SFCS.1996.548469
 |isbn = 0-8186-7594-2
 |s2cid = 39024286
 }}</ref>