Coloring bridge-free antiprismatic graphs
Cl\'eoph\'ee Robin, Eileen Robinson

TL;DR
This paper presents a polynomial-time algorithm for the clique cover problem in co-bridge-free prismatic graphs, a class of graphs for which the coloring problem's complexity was previously unresolved.
Contribution
It introduces a structural characterization of co-bridge-free prismatic graphs and leverages this to solve the clique cover problem efficiently.
Findings
Polynomial-time algorithm for clique cover in co-bridge-free prismatic graphs
Bounded number of disjoint triangles in these graphs
Application of existing structural theorems to solve the problem
Abstract
The coloring problem is a well-research topic and its complexity is known for several classes of graphs. However, the question of its complexity remains open for the class of antiprismatic graphs, which are the complement of prismatic graphs and one of the four remaining cases highlighted by Lozin and Malishev. In this article we focus on the equivalent question of the complexity of the clique cover problem in prismatic graphs. A graph is prismatic if for every triangle of , every vertex of not in has a unique neighbor in . A graph is co-bridge-free if it has no as induced subgraph. We give a polynomial time algorithm that solves the clique cover problem in co-bridge-free prismatic graphs. It relies on the structural description given by Chudnovsky and Seymour, and on later work of Preissmann, Robin and Trotignon. We show that co-bridge-free…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · graph theory and CDMA systems
