Selected Publications and Papers, Joel Foisy


  • Intrinsically linked signed graphs in projective space, Discrete Math. 312 (2012), no. 12-13, 2009-2022.

  • 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.