On off-diagonal ordered Ramsey numbers of nested matchings

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On off-diagonal ordered Ramsey numbers of nested matchings

Popis výsledku v původním jazyce

For two graphs G&lt; and H&lt; with linearly ordered vertex sets, the ordered Ramsey number r&lt;(G&lt;, H&lt;) 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&lt; or a blue copy of H&lt;. For a positive integer n, a nested matching NMn&lt; 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&lt;(NMn&lt;, K3&lt;) obtained by Rohatgi, we disprove his conjecture by showing 4n + 1 &lt;= r&lt;(NMn&lt;, K3&lt; ) &lt;= (3 + root 5)n + 1 for every n &gt;= 6, and we determine the numbers r&lt;(NMn&lt;, K3&lt;) 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 &gt;= 3. We also prove r&lt;(NMm&lt;, Kn&lt; ) =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.

Název v anglickém jazyce

On off-diagonal ordered Ramsey numbers of nested matchings

Popis výsledku anglicky

For two graphs G&lt; and H&lt; with linearly ordered vertex sets, the ordered Ramsey number r&lt;(G&lt;, H&lt;) 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&lt; or a blue copy of H&lt;. For a positive integer n, a nested matching NMn&lt; 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&lt;(NMn&lt;, K3&lt;) obtained by Rohatgi, we disprove his conjecture by showing 4n + 1 &lt;= r&lt;(NMn&lt;, K3&lt; ) &lt;= (3 + root 5)n + 1 for every n &gt;= 6, and we determine the numbers r&lt;(NMn&lt;, K3&lt;) 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 &gt;= 3. We also prove r&lt;(NMm&lt;, Kn&lt; ) =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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GJ19-04113Y" target="_blank" >GJ19-04113Y: Pokročilé nástroje v kombinatorice, topologii a příbuzných oblastech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Discrete Mathematics

ISSN

0012-365X

e-ISSN

1872-681X

Svazek periodika

346

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

13

Strana od-do

113223

Kód UT WoS článku

000884801300003

EID výsledku v databázi Scopus

2-s2.0-85141336473