On total coloring of small fullerene nanodiscs - Cruz, Mariana M. F. da; Figueiredo, Celina M. H. de; Sasaki, Diana; Castonguay, Diane (Anais do Encontro de Teoria da Computação (ETC); 2023: Anais do VIII Encontro de Teoria da Computação, 2023)
We investigate the total coloring of fullerene nanodiscs, a subclass of cubic planar graphs with girth 5 arising in Chemistry, motivated by a conjecture about the nonexistence of a Type 2 cubic graph of girth at least 5. We prove an auxiliary lemma which says that every central layer of a fullerene nanodisc is 4-total colorable, a necessary condition for the nanodisc to be Type 1, and we contribute by giving 4-total colorings for small fullerene nanodiscs, showing that these graphs are Type 1.