A note on graph burning of path forests
Document Type
Article
Publication Date
1-1-2024
Abstract
Graph burning is a natural discrete graph algorithm inspired by the spread of social contagion. Despite its simplicity, some open problems remain steadfastly unsolved, notably the burning number conjecture, which says that every connected graph of order m2 has burning number at most m. Earlier, we showed that the conjecture also holds for a path forest, which is disconnected, provided each of its paths is sufficiently long. However, finding the least sufficient length for this to hold turns out to be nontrivial. In this note, we present our initial findings and conjectures that associate the problem to some naturally impossibly burnable path forests. It is noteworthy that our problem can be reformulated as a topic concerning sumset partition of integers.
Keywords
discrete graph algorithm, burning number conjecture, spread of social contagion, sumset partition of integers, well-burnable
Divisions
MathematicalSciences
Funders
Malaysian Ministry of Higher Education for Fundamental Research Grant Scheme (FRGS/1/2023/STG06/USM/02/7)
Publication Title
Discrete Mathematics and Theoretical Computer Science
Volume
26
Issue
3
Publisher
Discrete Mathematics Theoretical Computer Science
Publisher Location
62 RUE DU CARDINAL MATHIEU, F-54000 NANCY, FRANCE