A note on a series of families constructed over the Cyclic graph

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:157

Article

Majumder, Kaushik¹  Mukherjee, Satyaki² 

[1] Indian Stat Inst, RC Bose Ctr Cryptol & Secur, 202 Barrackpore Trunk Rd, Kolkata 700108, India

[2] Univ Calif Berkeley, Dept Math, 970 Evans Hall, Berkeley, CA 94720 USA

关键词: Uniform hypergraph;    Intersecting family of k-sets;    Blocking set;    Transversal;   

DOI  :  10.1016/j.jcta.2018.02.001

来源: Elsevier

【 摘 要 】

Paul Erdos and Laszlo Lovisz established by means of an example that there exists a maximal intersecting family of k-sets with [(e-1)k!]blocks, where e is the base of natural logarithm. Laszlo Lovidsz conjectured that their example is best known example which has the maximum number of blocks. Later it was disproved. But the quest for such examples remain valid till this date. In this note we compute the transversal size of a certain series of intersecting families of k-sets, which is constructed over the Cyclic graph. It helps to provide an example of maximal intersecting family of k-sets with so many blocks and to present two worthwhile examples which disprove two special cases of one of the conjectures of Franld et al. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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