On monophonic position sets in graphs

Thomas, Elias John; Chandran S.V., Ullas; Tuite, James and Di Stefano, Gabriele (2023). On monophonic position sets in graphs. Discrete Applied Mathematics (Early Access).

DOI: https://doi.org/10.1016/j.dam.2023.02.021

Abstract

The general position problem in graph theory asks for the largest set S of vertices of a graph G such that no shortest path of G contains more than two vertices of S. In this paper we consider a variant of the general position problem called the monophonic position problem, obtained by replacing ‘shortest path’ by ‘induced path’. We prove some basic properties and bounds for the monophonic position number of a graph and determine the monophonic position number of some graph families, including unicyclic graphs, complements of bipartite graphs and split graphs. We show that the monophonic position number of triangle-free graphs is bounded above by the independence number. We present realisation results for the general position number, monophonic position number and monophonic hull number. Finally we discuss the complexity of the monophonic position problem.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 88147
• Item Type
• Journal Item
• ISSN
• 0166-218X
• Keywords
• General position set; General position number; Monophonic position set; Monophonic position number
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2023 The Authors
• Depositing User
• ORO Import