This paper discusses the complete structure of the (bull, diamond)-free graphs. As an application of that, we give the characterization of the partitionable (bull, diamond)-free graphs. Moreover, we show that such a partition for a partitionable (bull, diamond)-free graph can be found in polynomial time. Additionally, we show that the cop number of a (bull, diamond)-free graph containing a triangle is at most two less than its diameter. Furthermore, the cop number of a connected (Pn, bull, diamond)-free graph with a triangle, is at most n−3, for any natural number n>3. We also discuss a couple of applications of the structural theorem of the (bull, diamond)-free graphs in the conclusions.
@article{arxiv.2107.03750,
title = {Structure of (bull, diamond)-free graphs and its applications},
author = {Suchismita Mishra},
journal= {arXiv preprint arXiv:2107.03750},
year = {2024}
}