Defective incidence coloring of graphs - Bi, Huimin; Zhang, Xin (Applied mathematics and computation, 2023)
•Proper incidence coloring of graphs is generalized as defective incidence coloring of graphs.•Fast algorithms for constructing the optimal defective incidence colorings of certain graphs are presented.•Relation between the 1-defective incidence (n−1)-coloring and Latin square of order n is given. We define the d-defective incidence chromatic number of a graph, generalizing the notion of incidence chromatic number, and determine it for some classes of graphs including trees, complete bipartite graphs, complete graphs, and outerplanar graphs. Fast algorithms for constructing the optimal d-defective incidence colorings of those graphs are presented.