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The ramsey numbers for stripes and one complete graph

✍ Scribed by Peter Lorimer

Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
244 KB
Volume
8
Category
Article
ISSN
0364-9024

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✦ Synopsis

The Ramsey numbers M,,, n,P,, ..., n,P,), p > 2, are calculated.

1. Introduction

One class of generalized Ramsey numbers that are known exactly are those for the graphs nP2 which consist of n disjoint paths of length 2; E. J. Cockayne and the author proved in 111 that d r(nlp2, ..., n d P 2 ) = n, + I + C(n, -1) j -I

where n, = max(nl, ..., n d ) . This result is now extended to the Ramsey number r(Kp, nlP2, ..., ndP2) where p > 2 and K, is a complete graph with p vertices. Two cases need to be considered, depending on whether d < p or d 2 p and these are the subjects of two theorems. Theorem 1. If d < p , p > 2, and n , , ..., nd are positive, then Theorem 2. If d 3 p > 2 and nl 2 n2 3 1 . -3 nd > 0 then

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