Coloring Artemis graphs

TL;DR

This paper improves the efficiency of a graph coloring algorithm for Artemis graphs, a class characterized by the absence of certain subgraphs, achieving a better time complexity for coloring such graphs.

Contribution

It provides an improved implementation of a coloring algorithm specifically for Artemis graphs, reducing the time complexity to O(n^2m).

Findings

Coloring algorithm for Artemis graphs runs in O(n^2m) time.

The improved algorithm outperforms previous complexity bounds.

Applicable to graphs with no odd holes, antiholes, or prisms.

Abstract

We consider the class A of graphs that contain no odd hole, no antihole, and no ``prism'' (a graph consisting of two disjoint triangles with three disjoint paths between them). We show that the coloring algorithm found by the second and fourth author can be implemented in time O(n^2m) for any graph in A with n vertices and m edges, thereby improving on the complexity proposed in the original paper.