105 research outputs found
Independence numbers of hypergraphs with sparse neighborhoods
AbstractLet H be a hypergraph with N vertices and average degree d. Suppose that the neighborhoods of H are sparse, then its independence number is at least cN(logd /d), where c>0 is a constant. In particular, let integers r≥3 and n≥1 be fixed, and let H be r-uniform, triangle-free and linear, then its independence number is at least cNlognd/d for all sufficiently large d
Note on the degree sequences of k-hypertournaments
AbstractWe obtain a criterion for determining whether or not a non-decreasing sequence of non-negative integers is a degree sequence of some k-hypertournament on n vertices. This result generalizes the corresponding theorems on tournaments proposed by Landau [H.G. Landau, On dominance relations and the structure of animal societies. III. The condition for a score structure, Bull. Math. Biophys. 15 (1953) 143–148] in 1953
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 Score Sequences ofk-Hypertournaments
AbstractGiven two nonnegative integers n and k withn≥k> 1, a k -hypertournament on n vertices is a pair (V, A), where V is a set of vertices with | V | =n and A is a set of k -tuples of vertices, called arcs, such that for any k -subset S ofV , A contains exactly one of the k!k -tuples whose entries belong to S. We show that a nondecreasing sequence (r1, r2,⋯ , rn) of nonnegative integers is a losing score sequence of a k -hypertournament if and only if for each j(1 ≤j≤n),with equality holding whenj=n. We also show that a nondecreasing sequence (s1,s2 ,⋯ , sn) of nonnegative integers is a score sequence of somek -hypertournament if and only if for each j(1 ≤j≤n),with equality holding whenj=n. Furthermore, we obtain a necessary and sufficient condition for a score sequence of a strong k -hypertournament. The above results generalize the corresponding theorems on tournaments
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
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
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