Let D = (V (D), A(D)) be a digraph. The competition graph of D, is the graph with vertex set V (D) and edge set {uv ∈ `V (D) 2 ́ : ∃w ∈ V (D),−→ uw,−→ vw ∈ A(D)}. The double competition graph of D, is the graph with vertex set V (D) and edge set {uv ∈ `V (D) 2 ́ : ∃w1, w2 ∈ V (D),−−→ uw1,−−→ vw1,−−→ w2u,−−→ w2v ∈ A(D)}. A poset of dimension at most two is a digraph whose vertices are some points ...
