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STICK AND RAMSEY NUMBERS OF TORUS LINKS

MARIBETH JOHNSON

Department of Mathematics, California State University, San Bernardino, 5500 University Pkwy, San Bernardino CA 92407, USA

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,

STACY NICOLE MILLS

Department of Mathematics, California State University, San Bernardino, 5500 University Pkwy, San Bernardino CA 92407, USA

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, and

Department of Mathematics, California State University, San Bernardino, 5500 University Pkwy, San Bernardino CA 92407, USA

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https://doi.org/10.1142/S0218216513500272Cited by:3 (Source: Crossref)

Abstract

An algorithm that produces polygonal cable links is described, and applications discussed. In particular, the stick numbers of T_p,q torus links are shown to be 4p for 2p < q ≤ 3p, and it is shown that, in general, . Further, it is shown that the Ramsey number of a link is at least the sum of its arc index and bridge number. Using these results, we relate the Ramsey, stick and crossing numbers of torus links, showing .

Keywords:

AMSC: 57M25

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Journal cover image

Vol. 22, No. 07

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History

Received 13 December 2012

Accepted 17 April 2013

Published: 21 June 2013

Keywords