Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor

Arnott Kidner, Eckhard Steffen, Weiqiang Yu

An $r$-regular graph is an $r$-graph, if every odd set of vertices is connected to its complement by at least $r$ edges. We prove for $r\in \{4,5\}$, every projective planar $r$-g…