Size Ramsey Numbers of Stars Versus 3-chromatic Graphs

Let be the star with n edges, be the triangle, and be the family of odd cycles. We establish the following bounds on the corresponding size Ramsey numbers.

The upper (constructive) bound disproves a conjecture of Erdős.

Also we show that provided is an odd cycle of length o(n) or is a 3-chromatic graph of order o(log n).

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Received May 28, 1999

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ID="*" Supported by an External Research Studentship, Trinity College, Cambridge, UK.

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Pikhurko, O. Size Ramsey Numbers of Stars Versus 3-chromatic Graphs. Combinatorica 21, 403–412 (2001). https://doi.org/10.1007/s004930100004

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  • AMS Subject Classification (2000) Classes:  05C35