ON ORDERED RAMSEY NUMBERS OF TRIPARTITE 3-UNIFORM HYPERGRAPHS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10453258" target="_blank" >RIV/00216208:11320/22:10453258 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=JxGzS2gVCU" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=JxGzS2gVCU</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/21M1404958" target="_blank" >10.1137/21M1404958</a>

Jazyk výsledku

angličtina

Název v původním jazyce

ON ORDERED RAMSEY NUMBERS OF TRIPARTITE 3-UNIFORM HYPERGRAPHS

Popis výsledku v původním jazyce

For an integer k &gt;= 2, an ordered k-uniform hypergraph H = (H, &lt;) is a k-uniform hypergraph H together with a fixed linear ordering &lt; of its vertex set. The ordered Ramsey number (R) over bar (H, G) of two ordered k-uniform hypergraphs H and G is the smallest N is an element of N such that every red-blue coloring of the hyperedges of the ordered complete k-uniform hypergraph K-N((k)) on N vertices contains a blue copy of H or a red copy of G. The ordered Ramsey numbers are quite extensively studied for ordered graphs, but little is known about ordered hypergraphs of higher uniformity. We provide some of the first nontrivial estimates on ordered Ramsey numbers of ordered 3-uniform hypergraphs. In particular, we prove that for all d, n is an element of N and for every ordered 3-uniform hypergraph H on n vertices with maximum degree d and with interval chromatic number 3 there is an epsilon = epsilon(d) &gt; 0 such that (R) over bar (H, H) &lt;= 2(O)(n(2)(-epsilon)). In fact, we prove this upper bound for the number (R) over bar (G, K-3((3))(n)), where G is an ordered 3-uniform hypergraph with n vertices and maximum degree d, and K-3((3))(n) is the ordered complete tripartite hypergraph with consecutive color classes of size n. We show that this bound is not far from the truth by proving (R) over bar (H, K-3((3))(n)) &gt;= 2(Omega(n log n)) for some fixed ordered 3-uniform hypergraph H.

Název v anglickém jazyce

ON ORDERED RAMSEY NUMBERS OF TRIPARTITE 3-UNIFORM HYPERGRAPHS

Popis výsledku anglicky

For an integer k &gt;= 2, an ordered k-uniform hypergraph H = (H, &lt;) is a k-uniform hypergraph H together with a fixed linear ordering &lt; of its vertex set. The ordered Ramsey number (R) over bar (H, G) of two ordered k-uniform hypergraphs H and G is the smallest N is an element of N such that every red-blue coloring of the hyperedges of the ordered complete k-uniform hypergraph K-N((k)) on N vertices contains a blue copy of H or a red copy of G. The ordered Ramsey numbers are quite extensively studied for ordered graphs, but little is known about ordered hypergraphs of higher uniformity. We provide some of the first nontrivial estimates on ordered Ramsey numbers of ordered 3-uniform hypergraphs. In particular, we prove that for all d, n is an element of N and for every ordered 3-uniform hypergraph H on n vertices with maximum degree d and with interval chromatic number 3 there is an epsilon = epsilon(d) &gt; 0 such that (R) over bar (H, H) &lt;= 2(O)(n(2)(-epsilon)). In fact, we prove this upper bound for the number (R) over bar (G, K-3((3))(n)), where G is an ordered 3-uniform hypergraph with n vertices and maximum degree d, and K-3((3))(n) is the ordered complete tripartite hypergraph with consecutive color classes of size n. We show that this bound is not far from the truth by proving (R) over bar (H, K-3((3))(n)) &gt;= 2(Omega(n log n)) for some fixed ordered 3-uniform hypergraph H.

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/GJ18-13685Y" target="_blank" >GJ18-13685Y: Teorie modelů a extrémální kombinatorika</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

1095-7146

Svazek periodika

36

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

214-228

Kód UT WoS článku

000778502000011

EID výsledku v databázi Scopus

2-s2.0-85130609169