On ordered Ramsey numbers of matchings versus triangles

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10490823" target="_blank" >RIV/00216208:11320/24:10490823 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=QeEckafwD_" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=QeEckafwD_</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.37236/12107" target="_blank" >10.37236/12107</a>

Result language
angličtina
Original language name
On ordered Ramsey numbers of matchings versus triangles
Original language description
For graphs G(<) and H-< with linearly ordered vertex sets, the ordered Ramsey number r(<)(G(<), H-<) is the smallest positive integer N such that any red-blue coloring of the edges of the complete ordered graph K-N(<) on N vertices contains either a blue copy of G(<) or a red copy of H-<. Motivated by a problem of Conlon, Fox, Lee, and Sudakov (2017), we study the numbers r(<)(M-<, K-3(<)) where M-< is an ordered matching on n vertices. We prove that almost all n-vertex ordered matchings M-< with interval chromatic number 2 satisfy r(<)(M-<, K-3(<)) is an element of Omega ((n/log n)(5/4)) and r(<)(M-<, K-3(<)) is an element of O(n(7/4)), improving a recent result by Rohatgi (2019). We also show that there are n-vertex ordered matchings M-< with interval chromatic number at least 3 satisfying r(<)(M-<, K-3(<)) is an element of Omega((n/log n)(4/3)), which asymptotically matches the best known lower bound on these off-diagonal ordered Ramsey numbers for general n -vertex ordered matchings.
Czech name
—
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
<a href="/en/project/GX23-04949X" target="_blank" >GX23-04949X: Fundamental questions of discrete geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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