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The ramsey number r(k1 + c4, k5 − e)

✍ Scribed by Yang Yuansheng; G. R. T. Hendry

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
129 KB
Volume
19
Category
Article
ISSN
0364-9024

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📜 SIMILAR VOLUMES

The ramsey number of k5 - e
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Off-diagonal and asymptotic results on the Ramsey number r(K2,m,K2,n)
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## Abstract An upper bound on the Ramsey number __r__(__K__~2,__n‐s__~,__K__~2,__n__~) where __s__ ≥ 2 is presented. Considering certain __r__(__K__~2,__n‐s__~,__K__~2,__n__~)‐colorings obtained from strongly regular graphs, we additionally prove that this bound matches the exact value of __r__(__K

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## Abstract Harary stated the conjecture that for any graph __G__ with __n__ edges and without isolated vertices __r__(__K__~3~,__G__) ⩽ 2__n__ + 1. Erdös, Faudree, Rousseau, and Schelp proved that __r__(__K__~3~,__G__) ⩽ ⌈8/3__n__⌉. Here we prove that __r__(__K__~3~,__G__) ⩽ ⌊5/2__n__⌋ −1 for __n_

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## Abstract The Ramsey number __R__(3, 8) can be defined as the least number __n__ such that every graph on __n__ vertices contains either a triangle or an independent set of size 8. With the help of a substantial amount of computation, we prove that __R__(3, 8)=28.