List edge and list total colorings of planar graphs without non-induced 7-cycles

Aijun Dong, Guizhen Liu, Guojun Li
2013 Discrete Mathematics & Theoretical Computer Science  
Graphs and Algorithms Giving a planar graph G, let χ'l(G) and χ"l(G) denote the list edge chromatic number and list total chromatic number of G respectively. It is proved that if G is a planar graph without non-induced 7-cycles, then χ'l(G)≤Δ(G)+1 and χ"l(G)≤Δ(G)+2 where Δ(G)≥7.
doi:10.46298/dmtcs.629 fatcat:i33o5qzosbcprfwn25qj4ssn34