![Sample our Bioscience journals, sign in here to start your access, Latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5925/TOC-Subject-Sample-2021-Bioscience.jpg"})
Abstract
The simplest graph drawing method is that of putting the vertices of a graph on a line (spine) and drawing the edges as half-circles on k half planes (pages). Such drawings are called k-page book drawings and the minimal number of edge crossings in such a drawing is called the k-page crossing number. In a one-page book drawing, all edges are placed on one side of the spine, and in a two-page book drawing all edges are placed either above or below the spine. The one- and two-page crossing numbers of a graph provide upper bounds for the standard planar crossing. In this paper, we derive the exact one-page crossing numbers for four-row meshes, present a new proof for the one-page crossing numbers of Halin graphs, and derive the exact two-page crossing numbers for circulant graphs . We also give explicit constructions of the optimal drawings for each kind of graph.
Acknowledgements
This research was done while the first author was at the Department of Computer Science, Loughborough University, supported by the EPSRC grant GR/S76694/01.