论文信息 - Dot Product Representations of Planar Graphs

Dot Product Representations of Planar Graphs

A graph G on n vertices is a k-dot product graph if there are vectors u1,..., un ∈ Rk, one for each vertex of G, such that uiT uj ≥ 1 if and only if ij ∈ E(G). Fiduccia, Scheinerman, Trenk and Zito (1998) asked whether every planar graph is a 3-dot product graph. We show that the answer is "no". On the other hand, every planar graph is a 4-dot product graph.

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