REPEATED PATTERNS IN PROPER COLORINGS

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

REPEATED PATTERNS IN PROPER COLORINGS

Popis výsledku v původním jazyce

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&apos;n(3/2) colors for some absolute constant c&apos; 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.

Název v anglickém jazyce

REPEATED PATTERNS IN PROPER COLORINGS

Popis výsledku anglicky

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&apos;n(3/2) colors for some absolute constant c&apos; 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.

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

2021

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

—

Svazek periodika

35

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

2249-2264

Kód UT WoS článku

000703464500038

EID výsledku v databázi Scopus

2-s2.0-85117248823