含C<sub>6</sub>和K<sub>n,n</sub>的多色二部Ramsey数

林启忠; 杜智华

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含C₆和K_n,n的多色二部Ramsey数

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- 含C₆和K_n,n的多色二部Ramsey数
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 28, Issue 4, Pages: 401-404(2011)
- 作者机构：
  
  1. 福州大学数学与计算机科学学院
  2. 新疆师范大学数学科学学院
- 作者简介：
- 基金信息：
- DOI：
  CLC： O157.5
- Published：2011
- 稿件说明：
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[1]林启忠,杜智华.含C_6和K_(n,n)的多色二部Ramsey数[J].新疆大学学报(自然科学版),2011,28(04):401-404.

林启忠, 杜智华. 含C₆和K_n,n的多色二部Ramsey数[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2011, 28(4): 401-404.
[1]林启忠,杜智华.含C_6和K_(n,n)的多色二部Ramsey数[J].新疆大学学报(自然科学版),2011,28(04):401-404. DOI：

林启忠, 杜智华. 含C₆和K_n,n的多色二部Ramsey数[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2011, 28(4): 401-404. DOI：

摘要

设多色二部Ramsey数brk(C6;Kn

n)是最小的正整数N使得对二部完全图KN

N的边进行k+1着色时

总存在前k色中某种单色的C6或者第k+1色的Kn

n.本文主要利用随机方法得到brk(C6;Kn

n)=Θlong33//22 n对k≥3都成立

并且得到br2(C6;Kn

n)≥c(nlolgoglo3g nn)3/2对充分大的n成立.

Abstract

Let brk(C6;Kn

n) be the smallest N such that if all edges of KN

N are colored by k +1 colors

then there is a monochromatic C6 in one of the first k colors or a monochromatic Kn

n in the last color.It is shown that brk(C6;Kn

n) = Θ long33//22 n for k ≥ 3

and br2(C6;Kn

n) ≥ c(nlolgoglo3g nn)3/2for large n.

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references

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含C6和Kn,n的多色二部Ramsey数

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摘要

Abstract

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含C₆和K_n,n的多色二部Ramsey数