CID 2003 Abstracts - Colourings, Independence and Domination
CID 2003 Abstracts - Colourings, Independence and Domination
CID 2003 Abstracts - Colourings, Independence and Domination
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24 abstracts<br />
NEW VALUES AND BOUNDS FOR MULTICOLOR RAMSEY<br />
NUMBERS<br />
Tomasz Dzido<br />
University of Gdańsk, Pol<strong>and</strong><br />
The Ramsey number R(G 1 , G 2 , G 3 ) is the smallest number n such that in<br />
every 3-coloring of the edges of complete graph K n with color red, blue <strong>and</strong><br />
green a red subgraph G 1 , a blue subgraph G 2 or a green subgraph G 3 occurs.<br />
In this note we consider Ramsey numbers R(P 3 , C k , C m ), where P 3 is the path<br />
on 3 vertices, <strong>and</strong> C i is the cycle on i vertices. In addition, we present new<br />
bounds for R(C k , C k , C k ) where k is even positive number. In this paper we<br />
will present new results in this field as well as some conjectures.<br />
Keywords: Ramsey numbers.
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