A Skew Version of the Loebl–Komlós–Sós Conjecture

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00477022" target="_blank" >RIV/67985807:_____/17:00477022 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/17:10368799
Result on the web
<a href="http://dx.doi.org/10.1016/j.endm.2017.07.031" target="_blank" >http://dx.doi.org/10.1016/j.endm.2017.07.031</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.endm.2017.07.031" target="_blank" >10.1016/j.endm.2017.07.031</a>

Result language
angličtina
Original language name
A Skew Version of the Loebl–Komlós–Sós Conjecture
Original language description
Loebl, Komlós, and Sós conjectured that any graph such that at least half of its vertices have degree at least k contains every tree of order at most k + 1. We propose a skew version of this conjecture. We consider the class of trees of order at most k + 1 of given skew, that is, such that the sizes of the colour classes of the trees have a given ratio. We show that our conjecture is asymptotically correct for dense graphs. The proof relies on the regularity method. Our result implies bounds on Ramsey number of several trees of given skew.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

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

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