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New bounds for the distance Ramsey number | | Andrey Kupavskii
; Andrei Raigorodskii
; Maria Titova
; | | Date: |
2 Jul 2013 | | Abstract: | In this paper we study the distance Ramsey number $R_{{it D}}(s,t,d)$. The
extit{distance Ramsey number} $R_{{it D}}(s,t,d) $ is the minimum number $n$
such that for any graph $ G $ on $ n $ vertices, either G contains an induced $
s $-vertex subgraph isomorphic to a distance graph in $ Real^d $ or $ ar {G}
$ contains an induced $ t $-vertex subgraph isomorphic to a distance graph in $
Real^d $. We obtain upper and lower bounds for $R_{{it D}}(s,s,d)$ which are
similar to the bounds for the classical Ramsey number $Rleft(left lceil
frac{s}{[d/2]}
ight
ceil, left lceil frac{s}{[d/2]}
ight
ceil
ight)$. | | Source: | arXiv, 1307.0843 | | Services: | Forum | Review | PDF | Favorites | |
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