3 citations · 4 across the 11 of their papers we have counts for
7 papers · 1 filter
A proof using Böhme's Lemma that no Petersen family graph has a flat embedding
Joel Foisy, Catherine Jacobs, Trinity Paquin +2
Sachs and Conway-Gordon used linking number and a beautiful counting argument to prove that every graph in the Petersen family is intrinsically linked (have a pair of disjoint cycl…
Conflict graphs of maximally planar subgraphs of Petersen family graphs
Joel Foisy, Justin Raimondi
The purpose of this paper is to show that all maximally planar subgraphs of graphs in the Petersen Family have associated conflict graphs unbalanced. All but three strong conflict…
A spatial version of Tutte's conflict graph
Joel Foisy
Tutte showed that a graph is planar if and only if the conflict graph associated to every cycle of is bipartite. We define a (not necessarily unique) signed conflict graph…
Intrinsically projectively linked graphs
Joel Foisy, Luis Ángel Topete Galván, Evan Knowles +3
A graph is intrinsically projectively linked (IPL) if its every embedding in projective space contains a nonsplit link. Some minor-minimal IPL graphs have been found previously. We…
Links in projective planar graphs
Joel Foisy, Luis Ángel Topete Galván, Evan Knowles +3
A graph is nonseparating projective planar if has a projective planar embedding without a nonsplit link. Nonseparating projective planar graphs are closed under taking mino…
Intrinsically spherical 3-linked graphs
Madeleine Burkhart, Andrew Castillo, Jonathan Doane +2
We exhibit several families of planar graphs that are minor-minimal intrinsically spherical -linked. A graph is intrinsically spherical 3-linked if it is planar graph that has,…