692 1 archive 2 disk0/00/00/06/92 2006-02-22 2008-09-18 11:08:59 2008-09-18 11:08:59 confpaper show 0 An actual topic in the graph drawing is the question how to draw two edge sets on the same vertex set, the so-called simultaneous drawing of graphs. The goal is to simultaneously find a nice drawing for both of the sets. It has been found out that only restricted classes of planar graphs can be drawn simultaneously using straight lines and without crossings within the same edge set. In this paper, we negatively answer one of the most often posted open questions namely whether any two trees with the same vertex set can be drawn simultaneously crossing-free in a straight line way. http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=3843&spage=201 Kaufmann Michael Vrto Imrich Geyer Markus September 12-14, 2005 Graph Drawing Limerick, Ireland Healy Patrick Healy, Patrick Nikolov Nikola S. Nikolov, Nikola S. pub 201-210 FALSE Springer FALSE Brass, P., Cenek, E., Duncan, A., Efrat, A., Erten, C, Ismailescu, D., Kobourov, S., Lubiw, A., Mitchell, J.S.B.: On Simultaneous Planar Graph Embeddings. Dehne F., Sack, J., Snid, M. (eds.): Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science, Vol. 2748. Springer, Berlin (2002) 243-255 Duncan, C.A., Eppstein, D., Kobourov, S.G.: The Geometric Thickness of Low Degree Graphs. In: Boissonant, J.-D., Snoeyink, J. (eds.): 23rd Annual Symp. on Computational geometry. ACM Press, New York (2004) 340-346 Erten, C., Kobourov, S.G.: Simultaneous Embedding of a Planar Graph and its Dual on the Grid. Bose, P., Morin, P. (eds.): 13th Intl. Symp. on Algorithms & Computation. Lecture Notes in Computer Science, Vol. 2518. Springer, Berlin (2002) 575-587 Erten, C., Kobourov, S.G., Le, V., Navabi, A.: Simultaneous Graph Drawing: Layout Algorithms and Visualization Schemes. Liotta, G. (ed.): 11th Intl. Symp. on Graph Drawing. Lecture Notes in Computer Science, Vol. 2912. Springer, Berlin (2003) 437-449 Erten, C., Kobourov, S.G.: Simultaneous Embedding of Planar Graphs with Few Bends. Pach, J. (ed.): 12th Intl. Symp. on Graph Drawing. Lecture Notes in Computer Science, Vol. 3383. Springer, Berlin (2004) 195-205 Kobourov, S.G., Pitta, C.: An Interactive Multi-User System for Simultaneous Graph Drawing. Pach, J. (ed.): 12th Intl. Symposium on Graph Drawing. Lecture Notes in Computer Science, Vol. 3383. Springer, Berlin (2004) 492-501 Z.500 M.900 P.720 G.490 G.560 published 2006 none