A Density Turán Theorem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00474851" target="_blank" >RIV/67985807:_____/17:00474851 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/jgt.22075" target="_blank" >http://dx.doi.org/10.1002/jgt.22075</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.22075" target="_blank" >10.1002/jgt.22075</a>

Result language
angličtina
Original language name
A Density Turán Theorem
Original language description
Let F be a graph that contains an edge whose deletion reduces its chromatic number. For such a graph F, a classical result of Simonovits from 1966 shows that every graph on n > n(0)(F) vertices with more than chi(F)-2/chi(F)-1. n(2)/2 edges contains a copy of F. In this article we derive a similar theorem for multipartite graphs. For a graph H and an integer l >= v(H), let d(l) (H) be the minimum real number such that every l-partite graph whose edge density between any two parts is greater than d(l)(H) contains a copy of H. Our main contribution in this article is to show that d(l) (H) = chi(H)-2/chi(H)-1 for all l >= l(0)(H) sufficiently large if and only if H admits a vertex-coloring with chi(H) - 1 colors such that all color classes but one are independent sets, and the exceptional class induces just a matching. When H is a complete graph, this recovers a result of Pfender (Combinatorica 32 (2012), 483-495). We also consider several extensions of Pfender's result.
Czech name
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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
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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