D. V. Karpov, “On spanning trees without vertices of degree 2 in plane triangulations”, Zap. Nauchn. Sem. POMI, 2018, Volume 475,Pages <nobr>93

On spanning trees without vertices of degree 2 in plane triangulations

D. V. Karpov^ab

^a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
^b St. Petersburg State University, Mathematics and Mechanics Faculty, St. Petersburg, Russia

Abstract: Let $G$ be a $2$-connected plane graph such that at most one its face is not a triangle. It is proved that $G$ has a spanning tree without vertices of degree $2$.

Key words and phrases: plane graph, triangulation, spanning tree.

UDC: 519.173.2, 519.172.1

Received: 26.11.2018