# Simona Bonvicini: Cubic graphs with perfect 1-factorizations

Date: 15. 1. 2012

Source: Discrete mathematics seminar

Source: Discrete mathematics seminar

Torek, 17. 1. 2012 od 10h do 12h, Plemljev seminar, Jadranska 19

**Povzetek:**A regular graph

*G*is perfectly 1-factorable (

*P*1

*F*, for short) if it possesses a 1-factorization

*F*such that the union of any two 1-factors of

*F*is a Hamiltonian cycle.

In 1962, Kotzig described a procedure to obtain all
perfectly 1-factorable cubic graphs starting from the
*θ*-graph (the graph consisting of two vertices and three
multiple edges between them). Unfortunately, his procedure does not
tell whether a cubic graph *G* is *P*1*F* or not. For this reason, we
investigate some large families of cubic graphs and give some
properties of *P*1*F* cubic graphs. We also show an alternative proof
of Kotzig's result.

This is joint work with Giuseppe Mazzuoccolo.