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A conjecture concerning Ramsey's theorem

✍ Scribed by Martin Erickson

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 204 KB
Volume: 126
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90284-4

No coin nor oath required. For personal study only.

✦ Synopsis

P(c, m). If the edges of a countable injinite complete graph G are exactly c-colored, then there exists a countable infinite complete subgraph H of G whose edges are exactly m-colored.

The purpose of this note is to inquire as to which pairs c, m of positive integers make P(c, m) a true statement.

2. Sufficient conditions

If m= 1, then P(c, m) is just Ramsey's theorem with the hypothesis strengthened from c-coloring to exact c-coloring, so P(c,m) is true a fortiori.

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