On ordered Ramsey numbers of bounded-degree graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10384907" target="_blank" >RIV/00216208:11320/19:10384907 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=X2u0qdc0Zh" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=X2u0qdc0Zh</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2018.06.002" target="_blank" >10.1016/j.jctb.2018.06.002</a>

Result language
angličtina
Original language name
On ordered Ramsey numbers of bounded-degree graphs
Original language description
An ordered graph is a pair G=(H,<) where H is a graph and < is a total ordering of its vertices. The ordered Ramsey number R(G) is the minimum number N such that every 2-coloring of the edges of the ordered complete graph on N vertices contains a monochromatic copy of G. We show that for every integer d >= 3, almost every d-regular graph satisfies R(G) >= n^(3/2-1/d)/(4log(n)log(log(n))) for every ordering of G. In particular, there are 3-regular graphs on n vertices for which the numbers R(G) are superlinear in n, regardless of the ordering G. This solves a problem of Conlon, Fox, Lee, and Sudakov. On the other hand, we prove that every graph on n vertices with maximum degree 2 admits an ordering G such that R(G) is linear in n. We also show that almost every ordered matching M with n vertices and with interval chromatic number two satisfies R(M) >= cn^2/log(n)^2 for some absolute constant c.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA14-14179S" target="_blank" >GA14-14179S: Algorithmic, structural and complexity aspects of configurations in the plane</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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