Gutin, Gregory (1993) Finding a longest path in a complete multipartite digraph. SIAM Journal on Discrete Mathematics, 6 (2).
Full text access: Open
A digraph obtained by replacing each edge of a complete $m$-partite graph with an arc or a pair of mutually opposite arcs with the same end vertices is called a complete $m$-partite digraph. An $O ( n^3 )$ algorithm for finding a longest path in a complete $m$-partite $( m \geq 2 )$ digraph with $n$ vertices is described in this paper. The algorithm requires time $O( n^{2.5} )$ in case of testing only the existence of a Hamiltonian path and finding it if one exists. It is simpler than the algorithm of Manoussakis and Tuza [SIAM J. Discrete Math., 3 (1990), pp. 537–543], which works only for $m = 2$. The algorithm implies a simple characterization of complete $m$-partite digraphs having Hamiltonian paths that was obtained for the first time in Gutin [Kibernetica (Kiev), 4 (1985), pp. 124–125] for $m = 2$ and in Gutin [Kibernetica (Kiev), 1(1988), pp. 107–108] for $ m \geq 2 $.
This is a Submitted version This version's date is: 1993 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/37a16b9b-b674-9ed0-bdbc-8b7cb439e179/4/
Deposited by Research Information System (atira) on 25-Jul-2012 in Royal Holloway Research Online.Last modified on 25-Jul-2012