New restrictions on defective coloring with applications to steinberg-type graphs

Graph Partitions Under Average Degree Constraint

“…In 1966, Lovász [32] showed that every graph G is (d 1 , • • • , d k )-colorable whenever (d 1 + 1) + • • • + (d k + 1) ≥ ∆(G) + 1 and equality is attained by the complete graphs. We refer the readers to [4,6,12,13,16,17,20,23,26,27,36] for improper coloring and [1,2,5,8,9,14,19,34,37] for defective coloring.…”