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Bipartite Dot Product Graphs, Sean Bailey, David E. Brown
Bipartite Dot Product Graphs, Sean Bailey, David E. Brown
Mathematics and Statistics Faculty Publications
Given a bipartite graph G = (X, Y, E), the bipartite dot product representation of G is a function f : X ∪Y → ℝk and a positive threshold t such that for any x ∈ X and y ∈ Y , xy ∈ E if and only if f(x) · f(y) ≥ t. The minimum k such that a bipartite dot product representation exists for G is the bipartite dot product dimension of G, denoted bdp(G). We will show that such representations exist for all bipartite graphs as well as give an upper bound for the bipartite dot …