Abstract
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. © 2011 Springer-Verlag.
Cite
CITATION STYLE
Kang, R. J., & Müller, T. (2011). Dot product representations of planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6502 LNCS, pp. 287–292). https://doi.org/10.1007/978-3-642-18469-7_26
Register to see more suggestions
Mendeley helps you to discover research relevant for your work.
