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On the use of senders in generalized ramsey theory for graphs

✍ Scribed by Stefan A Burr; Jaroslav Nešetřil; Vojtech Rödl

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
910 KB
Volume
54
Category
Article
ISSN
0012-365X

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✦ Synopsis

If F, G, and H are graphs, write F ~ (G,/-/) to mean that however the edges of F are colored red and blue, either the red (partial) subgraph contains a copy of G or the blue subgraph contains a copy of H. Many interesting questions exist concerning this relation, particularly involving the case in which F is minimal for this property. A useful tool for constructing graphs relevant to such questions, at least when G and H are 3-connected, is developed here, namely graphs called senders. These senders are used to prove a number of theorems about the class of minimal F, as well as various related results. For example, let each of G and H be 3-connected, or a triangle. Then there exists an a > 0 such that if n is sufficiently large, there are at least ca, log, nonisomorphic F such that F ---, ((3, H) in a minimal way.

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