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Ramsey Properties of Families of Graphs

✍ Scribed by Ronald Graham; Tomasz Łuczak; Vojtěch Rödl; Andrzej Ruciński

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
106 KB
Volume
86
Category
Article
ISSN
0095-8956

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✦ Synopsis

For a graph F and natural numbers a 1 ; . . . ; a r ; let F ! ða 1 ; . . . ; a r Þ denote the property that for each coloring of the edges of F with r colors, there exists i such that some copy of the complete graph K ai is colored with the ith color. Furthermore, we write ða 1 ; . . . ; a r Þ ! ðb 1 ; . . . ; b s Þ if for every F for which F ! ða 1 ; . . . ; a r Þ we have also F ! ðb 1 ; . . . ; b s Þ: In this note, we show that a trivial sufficient condition for the relation ða 1 ; . . . ; a r Þ ! ðb 1 ; . . . ; b s Þ is necessary as well. # 2002 Elsevier Science (USA)

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