Intersections of curve systems and the crossing number ofC 5 ×C 5

Autor:	R. B. Richter, C. Thomassen
Rok vydání:	1995
Předmět:	Combinatorics Discrete mathematics symbols.namesake Computational Theory and Mathematics Crossing number (knot theory) symbols Discrete Mathematics and Combinatorics Geometry and Topology Disjoint sets Cartesian product Theoretical Computer Science Mathematics
Zdroj:	Discrete & Computational Geometry. 13:149-159
ISSN:	1432-0444 0179-5376
DOI:	10.1007/bf02574034
Popis:	It[Figure not available: see fulltext.] and[Figure not available: see fulltext.] are two families of pairwise disjoint simple closed curves in the plane such that each curve in[Figure not available: see fulltext.] intersects each curve in[Figure not available: see fulltext.], then the total number of points of intersection in[Figure not available: see fulltext.] is at least 2(m?1)n, where[Figure not available: see fulltext.][Figure not available: see fulltext.], and this bound is best possible. We use this to show that the cartesian product of two 5-cycles has crossing number 15.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::eda24e0cf7d3f69bf2bc22f298be9ea4 https://doi.org/10.1007/bf02574034 Zobrazit plný text záznamu Full text from SpringerLink