On a colored Turan problem of Diwan and Mubayi

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F22%3A00128972" target="_blank" >RIV/00216224:14330/22:00128972 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.disc.2022.113003" target="_blank" >https://doi.org/10.1016/j.disc.2022.113003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2022.113003" target="_blank" >10.1016/j.disc.2022.113003</a>

Result language
angličtina
Original language name
On a colored Turan problem of Diwan and Mubayi
Original language description
Suppose that R (red) and B (blue) are two graphs on the same vertex set of size n, and H is some graph with a red-blue coloring of its edges. How large can R and B be if R∪B does not contain a copy of H? Call the largest such integer mex(n,H). This problem was introduced by Diwan and Mubayi, who conjectured that (except for a few specific exceptions) when H is a complete graph on k+1 vertices with any coloring of its edges mex(n,H)=ex(n,Kk+1). This conjecture generalizes Turán's theorem. Diwan and Mubayi also asked for an analogue of Erdős-Stone-Simonovits theorem in this context. We prove the following upper bound on the extremal threshold in terms of the chromatic number χ(H) and the reduced maximum matching number M(H) of H. [Formula presented] M(H) is, among the set of proper χ(H)-colorings of H, the largest set of disjoint pairs of color classes where each pair is connected by edges of just a single color. The result is also proved for more than 2 colors and is tight up to the implied constant factor. We also study mex(n,H) when H is a cycle with a red-blue coloring of its edges, and we show that [Formula presented], which is tight.
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
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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