Edge-ordered Ramsey numbers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10403061" target="_blank" >RIV/00216208:11320/19:10403061 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=WyEyhqaWsg" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=WyEyhqaWsg</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Edge-ordered Ramsey numbers
Original language description
We introduce and study a variant of Ramsey numbers foredge-orde-red graphs, that is, graphs with linearly ordered sets of edges. The edge-ordered Ramsey number Re(G) of an edge-ordered graph G is the minimum positive integer N such that there exists an edge-ordered complete graph K_N on N vertices suchthat every 2-coloring of the edges of K_N contains a monochromatic copy of G as an edge-ordered subgraph of K_N. We prove that the edge-ordered Ramsey number Re(G) is finite for every edge-ordered graph G and we obtain better estimates for special classes of edge-orderedgraphs. In particular, we prove Re(G) <= 2^(O(n^3 logn)) for every bipartite edge-orderedgraph G on n vertices. We also introduce a natural class of edge-orderings, calledlexicographic edge-orderings, for which we can prove much better upper bounds onthe corresponding edge-ordered Ramsey numbers.
Czech name
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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
10101 - Pure mathematics

Project
<a href="/en/project/GJ18-13685Y" target="_blank" >GJ18-13685Y: Model thoery and extremal combinatorics</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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