Every cycle-connected multipartite tournament has a universal arc

(Arc-disjoint) cycle packing in tournament: classical and parameterized complexity

Given a tournament T , the problem MaxCT consists of finding a maximum (arc-disjoint) cycle packing of T . In the same way, MaxTT corresponds to the specific case where the collection of cycles are triangles (i.e. directed 3-cycles). Although MaxCT can be seen as the LP dual of minimum feedback arc set in tournaments which have been widely studied, surprisingly no algorithmic results seem to ex...

On cycles through two arcs in strong multipartite tournaments

A multipartite tournament is an orientation of a complete c-partite graph. In [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007) 1148–1150], Volkmann proved that a strongly connected cpartite tournament with c > 3 contains an arc that belongs to a directed cycle of length m for every m ∈ {3, 4, . . . , c}. He also conjectu...

The number of kings in a multipartite tournament

We show that in any n-partite tournament, where n/> 3, with no transmitters and no 3-kings, the number of 4-kings is at least eight. All n-partite tournaments, where n/>3, having eight 4-kings and no 3-kings are completely characterized. This solves the problem proposed in Koh and Tan (accepted).

Every Body Has a Brain

[1] http://ebhb.morphonix.com/ [2] http://fireflyfoundation.wordpress.com/brain-games/every-body-has-a-brain/ [3] http://dev.cdgr.ucsb.edu/organizations/morphonix [4] http://dev.cdgr.ucsb.edu/category/genre/educational [5] http://dev.cdgr.ucsb.edu/category/genre/music/dance [6] http://dev.cdgr.ucsb.edu/category/topics/anatomy [7] http://dev.cdgr.ucsb.edu/category/topics/brain [8] http://dev.cdg...

Every Algorithm Has a POV