Exact Crossing Number Parameterized by Vertex Cover

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00108274" target="_blank" >RIV/00216224:14330/19:00108274 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-030-35802-0_24" target="_blank" >http://dx.doi.org/10.1007/978-3-030-35802-0_24</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-35802-0_24" target="_blank" >10.1007/978-3-030-35802-0_24</a>

Result language
angličtina
Original language name
Exact Crossing Number Parameterized by Vertex Cover
Original language description
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.
Czech name
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Czech description
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Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA17-00837S" target="_blank" >GA17-00837S: Structural properties, parameterized tractability and hardness in combinatorial problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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