On off-diagonal ordered Ramsey numbers of nested matchings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10453203" target="_blank" >RIV/00216208:11320/23:10453203 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=i_~JwXZhwC" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=i_~JwXZhwC</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2022.113223" target="_blank" >10.1016/j.disc.2022.113223</a>

Result language
angličtina
Original language name
On off-diagonal ordered Ramsey numbers of nested matchings
Original language description
For two graphs G< and H< with linearly ordered vertex sets, the ordered Ramsey number r<(G<, H<) is the minimum N such that every red-blue coloring of the edges of the ordered complete graph on N vertices contains a red copy of G< or a blue copy of H<. For a positive integer n, a nested matching NMn< is the ordered graph on 2n vertices with edges {i, 2n - i + 1} for every i = 1, ... , n. We improve bounds on the ordered Ramsey numbers r<(NMn<, K3<) obtained by Rohatgi, we disprove his conjecture by showing 4n + 1 <= r<(NMn<, K3< ) <= (3 + root 5)n + 1 for every n >= 6, and we determine the numbers r<(NMn<, K3<) exactly for n = 4, 5. As a corollary, this gives stronger lower bounds on the maximum chromatic number of k-queue graphs for every k >= 3. We also prove r<(NMm<, Kn< ) =O(mn) for arbitrary m and n. We expand the classical notion of Ramsey goodness to the ordered case and we attempt to characterize all connected ordered graphs that are n-good for every n is an element of N. In particular, we discover a new class of ordered trees that are n-good for every n is an element of N, extending all the previously known examples.(c) 2022 Elsevier B.V. All rights reserved.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
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/GJ19-04113Y" target="_blank" >GJ19-04113Y: Advanced tools in combinatorics, topology and related areas</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)