14 research outputs found
Score lists in multipartite hypertournaments
Given non-negative integers and with , an
--partite hypertournament on
vertices is a -tuple ,
where are vertex sets with , and is a set of
-tuples of vertices, called arcs, with exactly
vertices from , such that any
subset of , contains
exactly one of the -tuples
whose entries belong to . We obtain necessary and
sufficient conditions for lists of non-negative integers in non-decreasing
order to be the losing score lists and to be the score lists of some
-partite hypertournament
On Scores, Losing Scores and Total Scores in Hypertournaments
A -hypertournament is a complete -hypergraph with each -edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a -hypertournament, the score (losing score ) of a vertex is the number of arcs containing in which is not the last element (in which is the last element). The total score of is defined as . In this paper we obtain stronger inequalities for the quantities , and , where . Furthermore, we discuss the case of equality for these inequalities. We also characterize total score sequences of strong -hypertournaments
On vertex independence number of uniform hypergraphs
Abstract
Let H be an r-uniform hypergraph with r ≥ 2 and let α(H) be its vertex independence number. In the paper bounds of α(H) are given for different uniform hypergraphs: if H has no isolated vertex, then in terms of the degrees, and for triangle-free linear H in terms of the order and average degree.</jats:p