Multiplicities of subgraphs

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F96%3A00150787" target="_blank" >RIV/68407700:21340/96:00150787 - isvavai.cz</a>
Výsledek na webu
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DOI - Digital Object Identifier
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Jazyk výsledku
angličtina
Název v původním jazyce
Multiplicities of subgraphs
Popis výsledku v původním jazyce
A former conjecture of Burr and Rosta, extending a conjecture of Erdos, asserted that in any two-colouring of the edges of a large complete graph, the proportion of subgraphs isomorphic to a fixed graph G which are monochromatic is at least the proportion found in a random colouring. It is now known that the conjecture fails for some graphs G, including G=K-p for p greater than or equal to 4. We investigate for which graphs G the conjecture holds. Our main result is that the conjecture fails if G contains K-4 as a subgraph, and in particular it fails for almost all graphs.
Název v anglickém jazyce
Multiplicities of subgraphs
Popis výsledku anglicky
A former conjecture of Burr and Rosta, extending a conjecture of Erdos, asserted that in any two-colouring of the edges of a large complete graph, the proportion of subgraphs isomorphic to a fixed graph G which are monochromatic is at least the proportion found in a random colouring. It is now known that the conjecture fails for some graphs G, including G=K-p for p greater than or equal to 4. We investigate for which graphs G the conjecture holds. Our main result is that the conjecture fails if G contains K-4 as a subgraph, and in particular it fails for almost all graphs.

Projekt
<a href="/cs/project/GA201%2F94%2F0708" target="_blank" >GA201/94/0708: Stabilita a nestabilita v kvantových systémech.</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění
1996
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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