Fractional total colourings of graphs of high girth

Abstrakt

We prove that every graph with even maximum degree at least four or with maximum degree three that has a sufficiently large girth has total fractional chromatic number at most the most the maximum degree increased by one which confirms a conjecture of Reed for the considered graphs.

Klíčová slova

• fractional colorings
• total colorings
• large girth
• cubic graphs