TY - JOUR
T1 - Covers in 4-uniform Intersecting Families with Covering Number Three
AU - Chiba, Shuya
AU - Furuya, Michitaka
AU - Matsubara, Ryota
AU - Takatou, Masanori
PY - 2012/6
Y1 - 2012/6
N2 - Let k be an integer. In [3,4], Frankl, Ota and Tokushige proved that the maximum number of three-covers of a k-uniform intersecting family with covering number three is k3 - 3k2 + 6k - 4 for k = 3 or k ≥ 9, but the case 4 ≤ it ≤ 8 remained open. In this paper, we prove that the same holds for k = 4, and show that a 4-uniform family with covering number three which has 36 three-covers is uniquely determined.
AB - Let k be an integer. In [3,4], Frankl, Ota and Tokushige proved that the maximum number of three-covers of a k-uniform intersecting family with covering number three is k3 - 3k2 + 6k - 4 for k = 3 or k ≥ 9, but the case 4 ≤ it ≤ 8 remained open. In this paper, we prove that the same holds for k = 4, and show that a 4-uniform family with covering number three which has 36 three-covers is uniquely determined.
KW - Covering number
KW - Intersecting family
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U2 - 10.3836/tjm/1342701352
DO - 10.3836/tjm/1342701352
M3 - Article
AN - SCOPUS:84875161593
SN - 0387-3870
VL - 35
SP - 241
EP - 251
JO - Tokyo Journal of Mathematics
JF - Tokyo Journal of Mathematics
IS - 1
ER -