Defective incidence coloring of graphs

TL;DR

This paper introduces the concept of $d$-defective incidence chromatic number, generalizes existing graph coloring notions, and provides exact values and algorithms for specific graph classes.

Contribution

It defines the $d$-defective incidence chromatic number and determines it for various graph classes, along with presenting efficient coloring algorithms.

Findings

Determined the $d$-defective incidence chromatic number for trees, bipartite, complete, and outerplanar graphs.

Developed fast algorithms for constructing optimal $d$-defective incidence colorings.

Extended the theory of incidence coloring to include defect tolerance.

Abstract

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.