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@inproceedings{2243997,
author = {Hamm, Thekla and Hliněný, Petr},
address = {Dagstuhl, Germany},
booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)},
doi = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2022.46},
edition = {LIPIcs Vol. 224},
editor = {Goaoc, Xavier and Kerber, Michael},
keywords = {Crossing Number; Drawing Extension; Parameterised Complexity; Partial Planarity},
howpublished = {elektronická verze "online"},
language = {eng},
location = {Dagstuhl, Germany},
isbn = {978-3-95977-227-3},
pages = {"46:1"-"46:15"},
publisher = {Schloss Dagstuhl},
title = {Parameterised Partially-Predrawn Crossing Number},
url = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2022.46},
year = {2022}
}
TY - JOUR
ID - 2243997
AU - Hamm, Thekla - Hliněný, Petr
PY - 2022
TI - Parameterised Partially-Predrawn Crossing Number
PB - Schloss Dagstuhl
CY - Dagstuhl, Germany
SN - 9783959772273
KW - Crossing Number
KW - Drawing Extension
KW - Parameterised Complexity
KW - Partial Planarity
UR - http://dx.doi.org/10.4230/LIPIcs.SoCG.2022.46
N2 - Inspired by the increasingly popular research on extending partial graph drawings, we propose a new perspective on the traditional and arguably most important geometric graph parameter, the crossing number. Specifically, we define the partially predrawn crossing number to be the smallest number of crossings in any drawing of a graph, part of which is prescribed on the input (not counting the prescribed crossings). Our main result - an FPT-algorithm to compute the partially predrawn crossing number - combines advanced ideas from research on the classical crossing number and so called partial planarity in a very natural but intricate way. Not only do our techniques generalise the known FPT-algorithm by Grohe for computing the standard crossing number, they also allow us to substantially improve a number of recent parameterised results for various drawing extension problems.
ER -
HAMM, Thekla and Petr HLINĚNÝ. Parameterised Partially-Predrawn Crossing Number. Online. In Goaoc, Xavier and Kerber, Michael. \textit{38th International Symposium on Computational Geometry (SoCG 2022)}. LIPIcs Vol. 224. Dagstuhl, Germany: Schloss Dagstuhl, 2022, p.~''46:1''-''46:15'', 15 pp. ISBN~978-3-95977-227-3. Available from: https://dx.doi.org/10.4230/LIPIcs.SoCG.2022.46.
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