Maximal intersection critical families of finite sets

Autor:	N. Zagaglia Salvi
Rok vydání:	1996
Předmět:	Combinatorics Discrete mathematics Intersection Intersection curve Complete intersection Discrete Mathematics and Combinatorics Pairwise comparison Projective plane Fixed point Finite intersection property Finite set Theoretical Computer Science Mathematics
Zdroj:	Discrete Mathematics. 155:267-269
ISSN:	0012-365X
DOI:	10.1016/0012-365x(94)00391-u
Popis:	A finite family of pairwise intersecting r-sets is a maximal r-clique if it cannot be extended to another r-clique by adding a new r-set. It is intersection critical if it is not possible to replace any edge by some of its proper subsets, without violating the intersection property. We prove that if a maximal r-clique H , distinct from Kr+1r is not intersection critical, then | H | > | V ( H ) | . Moreover, we prove that the system of lines of a projective plane not passing through a fixed point is an intersection critical r-clique, not contained in any larger one.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::be1f27f886d3037930b570a870bd8d4a https://doi.org/10.1016/0012-365x(94)00391-u Zobrazit plný text záznamu Full Text from ScienceDirect