On the 3BD-closed set B3( 4, 5 )
On the 3BD-closed set B3( 4, 5 )
复制标题
DOI：
10.1016/j.disc.2004.06.009
复制
发表时间：
2004-10
期刊：
影响因子：
--
通讯作者：
L. Ji
中科院分区：
文献类型：
--
作者：
L. Ji
Let B3(K)={v:∃S(3,K,v)}. For K={4} or {4,6}, B3(K) has been determined by Hanani. In this paper, we investigate the case of K={4,5}. It is easy to see that if v∈B3({4,5}), then v≡1,2,4,5,8,10(mod12). It is known that B3({4})={v>0:v≡2,4(mod6)}⊂B3({4,5}) by Hanani and that {v>0:v≡5(mod12)}⊂B3({4,5}) by a previous paper of the author. We shall focus on the case of v≡1(mod12). It is proved that B3({4,5})={v>0:v≡1,2,4,5,8,10(mod12) and v≠13}.
Let B3(K)={v:∃S(3,K,v)}. For K={4} or {4,6}, B3(K) has been determined by Hanani. In this paper, we investigate the case of K={4,5}. It is easy to see that if v∈B3({4,5}), then v≡1,2,4,5,8,10(mod12). It is known that B3({4})={v>0:v≡2,4(mod6)}⊂B3({4,5}) by Hanani and that {v>0:v≡5(mod12)}⊂B3({4,5}) by a previous paper of the author. We shall focus on the case of v≡1(mod12). It is proved that B3({4,5})={v>0:v≡1,2,4,5,8,10(mod12) and v≠13}.