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arXiv · 2107.03750

Structure of (bull, diamond)-free graphs and its applications

Suchismita Mishra
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Abstract

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 ($P_n$, 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.

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Suchismita Mishra. 2021-07-08. Structure of (bull, diamond)-free graphs and its applications. https://arxiv.org/abs/2107.03750

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