منابع مشابه
New Lower Bound for Multicolor Ramsey Numbers for Even Cycles
For given finite family of graphs G1, G2, . . . , Gk, k ≥ 2, the multicolor Ramsey number R(G1, G2, . . . , Gk) is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors then there is always a monochromatic copy of Gi colored with i, for some 1 ≤ i ≤ k. We give a lower bound for k−color Ramsey number R(Cm, Cm, . . . , Cm), where m ≥ ...
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The well-known Moore bound M(k, g) serves as a universal lower bound for the order of k-regular graphs of girth g. The excess e of a k-regular graph G of girth g and order n is the difference between its order n and the corresponding Moore bound, e = n −M(k, g). We find infinite families of parameters (k, g), g > 6 and even, for which we show that the excess of any k-regular graph of girth g is...
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ژورنال
عنوان ژورنال: Science
سال: 2012
ISSN: 0036-8075,1095-9203
DOI: 10.1126/science.336.6081.521-a