Selected Publications and Papers, Joel Foisy

  • 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. 1 (2001); 437-482.

    Preprints:

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

  • Intrinsically knottable and linkable graphs , with former REU '04 students Amy DeCelles, Chad Versace, and Alice Wilson. (accepted for publication in Involve.)

    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.

    There are also some papers forthcoming from my REU '05 and '07 groups, but they are top secret at this point.