166
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Design and serial construction of digraph braids

Pages 17-26 | Received 07 Aug 2012, Accepted 28 Nov 2014, Published online: 05 Feb 2015

References

  • C.C. Adams, The Knot Book, American Mathematical Society, Providence, RI, 2004. An elementary introduction to the mathematical theory of knots, revised reprint of the 1994 original.
  • J.W. Alexander and G.B. Briggs, On types of knotted curves, Ann. Math. (2), 28 (1–4) (1926/27), pp. 562–586.
  • E. Artin, Theorie der Zöpfe, Abh. Math. Semin. Univ. Hambg. 4 (1925), pp. 47–72.
  • J. Bang-Jensen and C. Thomassen, A polynomial algorithm for the 2-path problem for semicomplete digraphs, SIAM J. Discrete Math. 5 (3) (1992), pp. 366–376.
  • H. Brunn, Über Verkettung, S.-B. Bayer. Akad. Wiss. Math-Phys. Klasse 22 (1892), pp. 77–99.
  • J. Carey, Creative Kumihimo, Carey Company, 1994.
  • J. Carey, Kumihimo connections, in ISAMA 99, N.A. Friedman and J. Barrallo, eds., Universidad del Pais Vasco, San Sebastián, Devon, 1999, pp. 91–97.
  • J. Carey, Bridging the gap – a search for a braid language, in Bridges London: Mathematics, Music, Art, Architecture, Culture, R. Sarhangi and J. Sharp, eds., Tarquin Publications, London, 2006, pp. 61–68. Available at http://archive. bridgesmathart.org/2006/bridges2006-61.html.
  • R. Edwards, Bush Leatherwork, Rams Skull Press, Esk, Queensland, 1997.
  • P. Erdős and L. Moser, On the representation of directed graphs as unions of orderings, Magyar Tud. Akad. Mat. Kutató Int. Közl. 9 (1964), pp. 125–132.
  • R. Graumont and J. Hensel, Encyclopedia of Knots and Fancy Rope Work, Cornell Maritime Press, Atglen, PA, 1952.
  • V. Irvine and F. Ruskey, Developing a mathematical model for bobbin lace, J. Math. Arts 8 (3–4) (2014), pp. 95–110.
  • H. Levinson, Decomposable braids and linkages, Trans. Am. Math. Soc. 178 (1973), pp. 111–126.
  • H. Levinson, Decomposable braids as subgroups of braid groups, Trans. Am. Math. Soc. 202 (1975), pp. 51–55.
  • D. Morgan, Braiding Fine Leather: Techniques of the Australian Whipmakers, Cornell Maritime Press, Atglen, PA, 2002.
  • M. Muzychuk, A solution of the isomorphism problem for circulant graphs, Proc. Lond. Math. Soc. (3) 88 (1) (2004), pp. 1–41.
  • V. Neumann Lara, A short proof of a theorem of Reid and Parker on tournaments, Graphs Comb. 10 (4) (1994), pp. 363–366.
  • S. Nicoloso and U. Pietropaoli, Isomorphism testing for circulant graphs Cn(a, b), Util. Math. 87 (2012), pp. 165–182.
  • K.B. Reid and E.T. Parker, Disproof of a conjecture of Erdős and Moser on tournaments, J. Comb. Theory 9 (1970), pp. 225–238.
  • K. Reidemeister, Elementare begründung der knotentheorie, Abh. Math. Semin. Univ. Hambg. 5 (1927), pp. 24–32.
  • A. Sánchez-Flores, On tournaments and their largest transitive subtournaments, Graphs Comb. 10 (4) (1994), pp. 367–376.
  • A. Sanchez-Flores, On tournaments free of large transitive subtournaments, Graphs Comb. 14 (2) (1998), pp. 181–200.
  • W.D. Smith, The on-line encyclopedia of integer sequences. Available at http://oeis.org/A122027. Largest integer m so that every n-tournament contains a transitive (i.e. acyclic) subtournament with at least m vertices.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.