bibkey: wood2016threedimensional authors: David R. Wood year: 2016 title: Three-Dimensional Graph Drawing doi: 10.1007/978-1-4939-2864-4_656 url: https://research.monash.edu/en/publications/three-dimensional-graph-drawing/ claim: The chapter’s abstract gives the classical moment-curve straight-line grid drawing of a finite graph and distinguishes universal embeddability from optimizing drawing volume. strata_touched: [] license: citation-only triage: anchor

Universal drawing dimension and boundary width

Wood, Three-Dimensional Graph Drawing, in Ming-Yang Kao (ed.), Encyclopedia of Algorithms, second edition, Springer, pp. 2231–2236. The Monash publication record establishes the chapter metadata and DOI and includes its abstract.

The abstract explicitly calls the universal construction folklore and places vertex i at (i, i², i³), using non-coplanarity of four vertices to exclude crossings. The chapter interior was not obtained. The FIB boundary volume supplies its own Vandermonde proof, including non-collinearity of three vertices, exclusion of vertices inside edges, and exclusion of adjacent-edge overlap. It specifies finite simple graphs, since parallel edges and loops cannot be represented by distinct nondegenerate straight segments in this convention.

The result supplies existence of a drawing, not a bound on transport cost, edge length, wiring volume or elimination width. The FIB boundary volume’s complete-graph comparison uses this distinction directly.