Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: Outerplanar Crossing Numbers, the Circular Arrangement Problem and Isoperimetric Functions. | Outerplanar Crossing Numbers the Circular Arrangement Problem and Isoperimetric Functions Eva Czabarka Department of Mathematics The College of William Mary Williamsburg VA 23187 USA exczab@ László A. Szekelyi Department of Mathematics University of South Carolina Columbia SC 29208 USA szekely@ Ondrej Sykora Department of Computer Science Loughborough University Loughborough Leicestershire LE11 3TU UK Imrich Vrtó Department of Informatics Institute of Mathematics Slovak Academy of Sciences Dubravska 9 841 04 Bratislava Slovak Republic vrto@ Submitted Oct 31 2003 Accepted Nov 4 2004 Published Nov 12 2004 Mathematics Subject Classifications 05C62 68R10 Abstract We extend the lower bound in 15 for the outerplanar crossing number in other terminologies also called convex circular and one-page book crossing number to a more general setting. In this setting we can show a better lower bound for the outerplanar crossing number of hypercubes than the best lower bound for the planar crossing number. We exhibit further sequences of graphs whose outerplanar crossing number exceeds by a factor of log n the planar crossing number of the graph. We study the circular arrangement problem as a lower bound for the linear arrangement problem in a general fashion. We obtain new lower bounds for the circular arrangement problem. All the results depend on establishing good isoperimetric functions for certain classes of graphs. For several graph families new near-tight isoperimetric functions are established. This research was supported in part by the EPSRC grant GR S76694 01. iThis research was also supported in part by the NSF contracts Nr. 0072187 and 0302307. iThis research was supported in part by the VEGA grant No. 02 3164 23 THE ELECTRONIC JOURNAL OF COMBINATORICS 11 2004 R81 1 1 Introduction This paper is a sequel to our paper with Shahrokhi 15 . We use similar notation as in that paper G V G E G denotes a graph and dv denotes the .
