On $2$-extendability of generalized Petersen graphs

Abstract

Let $GP(n,k)$ be a generalized Petersen graph with $(n,k)=1$, $ n>k\geq4.$ Then every pair of parallel edges of $GP(n,k)$ is contained in a 1-factor of $GP(n,k)$. This partially answers a question posed by Larry Cammack and Gerald Schrag [Problem 101, Discrete Math. 73(3), 1989, 311-312].