Proof of the Katchalski-Lewis Transversal Conjecture for T(3)-Families of Congruent Discs

Autor:	Aladár Heppes
Rok vydání:	2007
Předmět:	Combinatorics Conjecture Computational Theory and Mathematics Transversal (combinatorics) Common line Discrete Mathematics and Combinatorics Geometry and Topology Disjoint sets Constant (mathematics) Theoretical Computer Science Mathematics
Zdroj:	Discrete & Computational Geometry. 38:289-304
ISSN:	1432-0444 0179-5376
DOI:	10.1007/s00454-007-1339-2
Popis:	A family of disjoint closed congruent discs is said to have property T(3) if to every triple of discs there exists a common line transversal. Katchalski and Lewis [10] proved the existence of a constant mdisc such that to every family of disjoint closed congruent discs with property T(3) a straight line can be found meeting all but at most mdisc of the members of the family. They conjectured that this is true even with mdisc = 2. On one hand Bezdek [1] proved mdisc ≥ 2 in 1991 and on the other hand Kaiser [9] showed mdisc ≤ 12 in a recent paper. The present work is devoted to proving this conjecture showing that mdisc ≤ 2.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3f3629362b605d85fc361a0b6ab8404a https://doi.org/10.1007/s00454-007-1339-2 Zobrazit plný text záznamu Full text from SpringerLink