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The connected Ramsey number

✍ Scribed by David P. Sumner

Book ID: 107748267
Publisher: Elsevier Science
Year: 1978
Tongue: English
Weight: 718 KB
Volume: 22
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90046-8

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## Abstract A graph __G__ is co‐connected if both __G__ and its complement __Ḡ__ are connected and nontrivial. For two graphs __A__ and __B__, the connected Ramsey number __r__~c~(__A, B__) is the smallest integer __n__ such that there exists a co‐connected graph of order __n__, and if __G__ is a c

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The planar Ramsey number \(P R(k, l)(k, l \geqslant 2)\) is the smallest integer \(n\) such that any planar graph on \(n\) vertices contains either a complete graph on \(k\) vertices or an independent set of size \(l\). We find exact values of \(P R(k, l)\) for all \(k\) and \(l\). Included is a pro