6
votes
2answers
182 views

Cubic graphs whose 2-factors all have the same cycle type

Let $G$ be a bridgeless cubic graph. I am interested in such graphs where all 2-factors are isomorphic (as graphs), i.e. have the same partition as cycle type. We'll say that this partition is ...
1
vote
2answers
425 views

when does a regular graph have a 1-factorization?

Is there a sufficient condition for a regular graph to have a 1-factorization (i.e. being able to pack all of its edges into disjoint perfect matchings, and excluding one vertex if the number of ...