Planar crossing numbers of genus g graphs (2006)
by
Hristo Djidjev
,
Imrich Vrtó
| Venue: | PROC. 33RD INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING , LECTURE NOTES IN COMPUTER SCIENCE 4051, PART I |
| Citations: | 5 - 0 self |
BibTeX
@INPROCEEDINGS{Djidjev06planarcrossing,
author = {Hristo Djidjev and Imrich Vrtó},
title = {Planar crossing numbers of genus g graphs},
booktitle = {PROC. 33RD INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING , LECTURE NOTES IN COMPUTER SCIENCE 4051, PART I},
year = {2006},
pages = {419--430},
publisher = {Springer– Verlag}
}
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Abstract
Pach and Tóth [15] proved that any n-vertex graph of genus g and maximum degree d has a planar crossing number at most c g dn, for a constant c>1. We improve on this results by decreasing the bound to O(dgn), if g = o(n), and to O(g²), otherwise, and also prove that our result is tight within a constant factor.
Citations
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