TY - JOUR

T1 - On a conjecture of erdöus, simonovits, and sós concerning anti‐Ramsey theorems

AU - Alon, Noga

PY - 1983

Y1 - 1983

N2 - For n ≧ k ≧ 3, let f(n,Ck) denote the maximum number m for which it is possible to color the edges of the complete graph Kn with m colors in such a way that each k‐cycle Ck in Kn has atleast two edges of the same color. Erdös, Simonovits, and Sós conjectured that for every fixed k ≧ 3, f(n, Ck) = n (k–2/2 + 1/k–1) + O(1), and proved it only for k = 3. It is shown that f(n, C4) = n + [1/3n] – 1, and the conjecture thus proved for k = 4. Some upper bounds are also obtained for f(n, Ck), k ≧ 5.

AB - For n ≧ k ≧ 3, let f(n,Ck) denote the maximum number m for which it is possible to color the edges of the complete graph Kn with m colors in such a way that each k‐cycle Ck in Kn has atleast two edges of the same color. Erdös, Simonovits, and Sós conjectured that for every fixed k ≧ 3, f(n, Ck) = n (k–2/2 + 1/k–1) + O(1), and proved it only for k = 3. It is shown that f(n, C4) = n + [1/3n] – 1, and the conjecture thus proved for k = 4. Some upper bounds are also obtained for f(n, Ck), k ≧ 5.

UR - http://www.scopus.com/inward/record.url?scp=84986495495&partnerID=8YFLogxK

U2 - 10.1002/jgt.3190070112

DO - 10.1002/jgt.3190070112

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AN - SCOPUS:84986495495

SN - 0364-9024

VL - 7

SP - 91

EP - 94

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 1

ER -