Toroidal grid minors and stretch in embedded graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F20%3A00114098" target="_blank" >RIV/00216224:14330/20:00114098 - isvavai.cz</a>
Result on the web
<a href="http://arxiv.org/abs/1403.1273" target="_blank" >http://arxiv.org/abs/1403.1273</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2019.05.009" target="_blank" >10.1016/j.jctb.2019.05.009</a>

Result language
angličtina
Original language name
Toroidal grid minors and stretch in embedded graphs
Original language description
We investigate the toroidal expanse of an embedded graph G, that is, the size of the largest toroidal grid contained in G as a minor. In the course of this work we introduce a new embedding density parameter, the stretch of an embedded graph G, and use it to bound the toroidal expanse from above and from below within a constant factor depending only on the genus and the maximum degree. We also show that these parameters are tightly related to the planar crossing number of G. As a consequence of our bounds, we derive an efficient constant factor approximation algorithm for the toroidal expanse and for the crossing number of a surface-embedded graph with bounded maximum degree.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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