2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/31951We prove that the geometric thickness of graphs whose maximum degree is no more than four is two. All of our algorithms run in O(n) time, where n is the number of vertices in the graph. In our proofs, we present an embedding algorithm for graphs with maximum degree three that uses an n x n grid and a more complex algorithm for embedding a graph with maximum degree four. We also show a variation using orthogonal edges for maximum degree four graphs that also uses an n x n grid. The results have implications in graph theory, graph drawing, and VLSI design.10 pages, 7 figures, submitted to SoCG 2004Computational GeometryDiscrete MathematicsI.3.5; F.2.2; G.2.2text