Strong 3‐Flow Conjecture for projective planar graphs

Obstruction Sets for Outer-Projective-Planar Graphs

A graph G is outer projective planar if it can be embedded in the projective plane so that every vertex appears on the boundary of a single face We exhibit obstruction sets for outer projective planar graphs with respect to the subdivision minor and Y orderings Equivalently we nd the minimal non outer projective planar graphs under these orderings

Erdös-Gyárfás Conjecture for Cubic Planar Graphs

In 1995, Paul Erdős and András Gyárfás conjectured that for every graph of minimum degree at least 3, there exists a non-negative integer m such that G contains a simple cycle of length 2m. In this paper, we prove that the conjecture holds for 3-connected cubic planar graphs. The proof is long, computer-based in parts, and employs the Discharging Method in a novel way.

K6-Minors in Projective Planar Graphs

It is shown that every 5-connected graph embedded in the projective plane with face-width at least 3 contains the complete graph on 6 vertices as a minor.

A characterization of projective-planar signed graphs

Internally 4-connected projective-planar graphs

5 Archdeacon proved that projective-planar graphs are characterized by 35 excluded minors. 6 Using this result we show that internally 4-connected projective-planar graphs are characterized 7 by 23 internally 4-connected excluded minors. 8