Covering by intersecting families

被引：4
|
作者：
Sanders, AJ [1 ]
机构：
[1] Univ Cambridge Trinity Coll, Cambridge CB2 1TQ, England
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES A | 2004年 / 108卷 / 01期
基金：
英国工程与自然科学研究理事会;
关键词：
D O I：
10.1016/j.jcta.2004.05.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A set family A subset of [n] ((k)) is called noncentred intersecting if it is intersecting but boolean ANDAis an element ofA A = 0; let L-k (n) be the least number of noncentred intersecting families which cover [n]((k)). We prove that for k greater than or equal to 3 fixed, L-k(n) = n(2)/2k(k -1) (1 + O(1/n)). (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：51 / 61
页数：11
相关论文
共 50 条
  • [1] Uniform intersecting families with covering number restrictions
    Frankl, P
    Ota, K
    Tokushige, N
    [J]. COMBINATORICS PROBABILITY & COMPUTING, 1998, 7 (01): : 47 - 56
  • [2] Uniform intersecting families with large covering number
    Frankl, Peter
    Kupavskii, Andrey
    [J]. EUROPEAN JOURNAL OF COMBINATORICS, 2023, 113
  • [3] A PROBLEM OF FUREDI AND SEYMOUR ON COVERING INTERSECTING FAMILIES BY PAIRS
    KAHN, J
    KALAI, G
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 1994, 68 (02) : 317 - 339
  • [4] The number of covers in intersecting families with covering number three
    Furuya, Michitaka
    Takatou, Masanori
    [J]. ARS COMBINATORIA, 2019, 142 : 293 - 327
  • [5] UNIFORM INTERSECTING FAMILIES WITH COVERING NUMBER-4
    FRANKL, P
    OTA, K
    TOKUSHIGE, N
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 1995, 71 (01) : 127 - 145
  • [6] Covers in 5-uniform intersecting families with covering number three
    Furuya, Michitaka
    Takatou, Masanori
    [J]. AUSTRALASIAN JOURNAL OF COMBINATORICS, 2013, 55 : 249 - 262
  • [7] Covers in 4-uniform Intersecting Families with Covering Number Three
    Chiba, Shuya
    Furuya, Michitaka
    Matsubara, Ryota
    Takatou, Masanori
    [J]. TOKYO JOURNAL OF MATHEMATICS, 2012, 35 (01) : 241 - 251
  • [8] COVERING INTERSECTING BI-SET FAMILIES UNDER MATROID CONSTRAINTS
    Berczi, Kristof
    Kiraly, Tamas
    Kobayashi, Yusuke
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2016, 30 (03) : 1758 - 1774
  • [9] On shadows of intersecting families
    Ahlswede, R
    Aydinian, H
    Khachatrian, LH
    [J]. COMBINATORICA, 2004, 24 (04) : 555 - 566
  • [10] Families intersecting on an interval
    Russell, Paul A.
    [J]. DISCRETE MATHEMATICS, 2009, 309 (09) : 2952 - 2956
12345