On nowhere dense graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10104609" target="_blank" >RIV/00216208:11320/11:10104609 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ejc.2011.01.006" target="_blank" >http://dx.doi.org/10.1016/j.ejc.2011.01.006</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2011.01.006" target="_blank" >10.1016/j.ejc.2011.01.006</a>
Alternative languages
Result language
angličtina
Original language name
On nowhere dense graphs
Original language description
In this paper, we define and analyze the nowhere dense classes of graphs. This notion is a common generalization of proper minor closed classes, classes of graphs with bounded degree, locally planar graphs, classes with bounded expansion, to name just afew classes which are studied extensively in combinatorial and computer science contexts. In this paper, we show that this concept leads to a classification of general classes of graphs and to the dichotomy between nowhere dense and somewhere dense classes. This classification is surprisingly stable as it can be expressed in terms of the most commonly used basic combinatorial parameters, such as the independence number a, the clique number omega, and the chromatic number x. The remarkable stability of this notion and its robustness has a number of applications to mathematical logic, complexity of algorithms, and combinatorics. We also express the nowhere dense versus somewhere dense dichotomy in terms of edge densities as a trichotomy t
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
European Journal of Combinatorics
ISSN
0195-6698
e-ISSN
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Volume of the periodical
32
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
18
Pages from-to
600-617
UT code for WoS article
000289132300009
EID of the result in the Scopus database
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