The double competition multigraph of a digraph

In this article, we introduce the notion of the double competition multigraph of a digraph. We give characterizations of the double competition multigraphs of arbitrary digraphs, loopless digraphs, reflexive digraphs, and acyclic digraphs in terms of edge clique partitions of the multigraphs.Comment: 9 page

Niche hypergraphs

If D = (V,A) is a digraph, its niche hypergraph Nℋ(D) = (V, ℰ) has the edge set ℰ = {ℯ ⊆ V | |e| ≥ 2 ∧ ∃ v ∈ V : e = ND-(v) ∨ ℯ = ND+(v)}. Niche hypergraphs generalize the well-known niche graphs (see [11]) and are closely related to competition hypergraphs (see [40]) as well as double competition hypergraphs (see [33]). We present several properties of niche hypergraphs of acyclic digraphs

The competition hypergraphs of doubly partial orders

Since Cho and Kim (2005) showed that the competition graph of a doubly partial order is an interval graph, it has been actively studied whether or not the same phenomenon occurs for other variants of competition graph and interesting results have been obtained. Continuing in the same spirit, we study the competition hypergraph, an interesting variant of the competition graph, of a doubly partial order. Though it turns out that the competition hypergraph of a doubly partial order is not always interval, we completely characterize the competition hypergraphs of doubly partial orders which are interval.Comment: 12 pages, 6 figure