REPEATED PATTERNS IN PROPER COLORINGS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438314" target="_blank" >RIV/00216208:11320/21:10438314 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=-2KtrFjtwh" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=-2KtrFjtwh</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1414103" target="_blank" >10.1137/21M1414103</a>

Result language
angličtina
Original language name
REPEATED PATTERNS IN PROPER COLORINGS
Original language description
For a fixed graph H, what is the smallest number of colors C such that there is a proper edge-coloring of the complete graph K-n with C colors containing no two vertex-disjoint color-isomorphic copies, or repeats, of H? We study this function and its generalization to more than two copies using a variety of combinatorial, probabilistic, and algebraic techniques. For example, we show that for any tree T there exists a constant c such that any proper edge-coloring of K-n with at most cn(2) colors contains two repeats of T, while there are colorings with at most c'n(3/2) colors for some absolute constant c' containing no three repeats of any tree with at least two edges. We also show that for any graph H containing a cycle there exist k and c such that there is a proper edge-coloring of K-n with at most cn colors containing no k repeats of H, while for a tree T with m edges, a coloring with o(n((m+1)/m)) colors contains omega(1) repeats of T.
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
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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