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A Ramsey-type problem and the Turan numbers D. S. Gunderson
 

Summary: A Ramsey-type problem and the TurŽan numbers
N. Alon
P. Erdos
D. S. Gunderson
M. Molloy§¶
28 February 2000
Abstract
For each n and k, we examine bounds on the largest number m so
that for any k-coloring of the edges of Kn there exists a copy of Km
whose edges receive at most k - 1 colors. We show that for k

n +
(n1/3
), the largest value of m is asymptotically equal to the TurŽan
number t(n, n
2 /k ), while for any constant > 0, if k (1 - )

n
then the largest m is asymptotically larger than that TurŽan number.
1 Introduction

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics