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@inproceedings{1646079,
author = {Hliněný, Petr and Sankaran, Abhisekh},
address = {Cham},
booktitle = {GD 2019: Graph Drawing and Network Visualization},
doi = {http://dx.doi.org/10.1007/978-3-030-35802-0_24},
keywords = {Graph drawing; Crossing number; Parameterized complexity; Vertex cover},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Cham},
isbn = {978-3-030-35801-3},
pages = {307-319},
publisher = {Springer, Lecture Notes in Computer Science, volume 11904},
title = {Exact Crossing Number Parameterized by Vertex Cover},
url = {http://dx.doi.org/10.1007/978-3-030-35802-0_24},
year = {2019}
}
TY - JOUR
ID - 1646079
AU - Hliněný, Petr - Sankaran, Abhisekh
PY - 2019
TI - Exact Crossing Number Parameterized by Vertex Cover
PB - Springer, Lecture Notes in Computer Science, volume 11904
CY - Cham
SN - 9783030358013
KW - Graph drawing
KW - Crossing number
KW - Parameterized complexity
KW - Vertex cover
UR - http://dx.doi.org/10.1007/978-3-030-35802-0_24
N2 - We prove that the exact crossing number of a graph can be efficiently computed for simple graphs having bounded vertex cover. In more precise words, Crossing Number is in FPT when parameterized by the vertex cover size. This is a notable advance since we know only very few nontrivial examples of graph classes with unbounded and yet efficiently computable crossing number. Our result can be viewed as a strengthening of a previous result of Lokshtanov [arXiv, 2015] that Optimal Linear Arrangement is in FPT when parameterized by the vertex cover size, and we use a similar approach of reducing the problem to a tractable instance of Integer Quadratic Programming as in Lokshtanov’s paper.
ER -
HLINĚNÝ, Petr a Abhisekh SANKARAN. Exact Crossing Number Parameterized by Vertex Cover. In \textit{GD 2019: Graph Drawing and Network Visualization}. Cham: Springer, Lecture Notes in Computer Science, volume 11904, 2019, s.~307-319. ISBN~978-3-030-35801-3. Dostupné z: https://dx.doi.org/10.1007/978-3-030-35802-0\_{}24.
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