On the Anti-Ramsey Threshold for Non-Balanced Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00382252" target="_blank" >RIV/68407700:21340/24:00382252 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.37236/11449" target="_blank" >https://doi.org/10.37236/11449</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.37236/11449" target="_blank" >10.37236/11449</a>

Result language
angličtina
Original language name
On the Anti-Ramsey Threshold for Non-Balanced Graphs
Original language description
For graphs G, H, we write G(->)(rb) H if for every proper edge-coloring of G there is a rainbow copy of H, i.e., a copy where no color appears more than once. Kohayakawa, Konstadinidis and the last author proved that the threshold for G(n, p) (rb)(->) H is at most n(-1)/m(2)(H). Previous results have matched the lower bound for this anti-Ramsey threshold for cycles and complete graphs with at least 5 vertices. Kohayakawa, Konstadinidis and the last author also presented an infinite family of graphs H for which the anti-Ramsey threshold is asymptotically smaller than n(-1)/m(2). In this paper, we devise a framework that provides a richer family of such graphs.
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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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