Selected Publications and Papers, Joel Foisy

  • When graph theory meets knot theory, with Lewis Ludwig, Communicating mathematics, 67--85, Contemp. Math., 479, Amer. Math. Soc., Providence, RI, 2009.

  • Intrinsically linked graphs in projective space. , with REU '07 and '08 students Jason Bustamante, Jared Federman, Kenji Kozai, Kevin Matthews, Kristin McNamara, Emily Stark, and Kristen Trickey, Algebr. Geom. Topol. 9 (2009), no. 3, 1255--1274.

  • Corrigendum to: ``Knotted Hamiltonian cycles in spatial embeddings of complete graphs'' New York J. Math. 13 (2007), 11--16;

  • On graphs for which every planar immersion lifts to a knotted spatial embedding, with REU '04 students Amy DeCelles, Chad Versace, and Alice Wilson, Involve 1 (2008), no. 2, 145--158.

  • Some results on intrinsically knotted graphs , with Tom Fleming and former REU '03 students Garry Bowlin, Paul Blain, Jacob Hendricks, and Jason LaCombe,J. Knot Theory Ramif., (16), no. 6 (2007); 749-760.

    Knotted Hamiltonian cycles in spatial embeddings of complete graphs , with former REU '03 students Garry Bowlin, Paul Blain, Jacob Hendricks, and Jason LaCombe, New York J. Math. (13), (2007); 11-16.

  • More intrinsically knotted graphs, Journal of Graph Theory (43), no. 2 (2007); 115- 124.

  • Graphs with a knot or a 3-component link in every spatial embedding , J. Knot Theory Ramif., (15), no. 9 (2006); 1113-1118.

  • Some new intrinsically 3- linked graphs, with former REU student ('01-'03) Garry Bowlin. J. Knot Theory Ramif., (13), no. 8 (2004); 1021-1027.

  • Graphs with disjoint links in every spatial embedding, with former REU '99 and '00 students Anton Dochtermann, Stephen Chan, Jennifer Hespen, Trent Lalonde, Quincy Looney, Eman Kunz, Katherine Sharrow and Nathan Thomas. J. Knot Theory Ramif., (13), no. 6 (2004); 737-748.

  • A newly recognized intrinsically knotted graph, Journal of Graph Theory (43), no. 3 (2003); 199-209.

  • Intrinsically knotted graphs, Journal of Graph Theory (39), no. 3 (2002); 178-187.

  • Intrinsically n-linked graphs, with Erica Flapan, Ramin Naimi, and James Pommersheim, Journal of Knot Theory and Its Ramifications (10) 2001, no. 8, 1143-1154.

  • The shortest enclosure of two connected regions in a corner, with former REU '97 students G. Christopher Hruska, Dmitriy Leykekhman, Daniel Pinzon, and Brian J. Shay; Rocky Mountain J. of Math., (31), no. 2 (2001); 437-482.

    Preprints:

    There is no REU 2011 paper, as I did not advise a group in 2011.

    The REU 2010 paper is being edited.

  • The REU 2009 paper has been submitted for publication. Here is a recent version of that paper.

  • Graphs that are intrinsically linked with an unused vertex , with former REU '01 students Garry Bowlin, Barbara Chervenka, and April Quinn.

    REU '06 group paper: Intrinsically $S^1$ 3-linked graphs and other aspects of $S^1$ embeddings . Published in the Rose-Hulman Undergraduate Mathmematics Journal, vol 8, issue 2, 2007.

    REU 2008 paper. (Submitted for publication)

    REU 2005 paper. (There are still other written results from 2005 year that require more editing).