A Note on Graph Burning of Path Forests

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 $m^2$ has burning number at most $m$. Earlier,...

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Vydané v:Discrete Mathematics and Theoretical Computer Science Ročník 26:3; číslo Discrete Algorithms; s. 1 - 13
Hlavní autori: Tan, Ta Sheng, Teh, Wen Chean
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Nancy DMTCS 01.10.2024
Discrete Mathematics & Theoretical Computer Science
Predmet:
05c85, 05a17, 68r10
Algorithms
Forests
Mathematical research
mathematics - combinatorics
Methods
Path analysis
Trees (Graph theory)
Malaysia
ISSN:1365-8050, 1462-7264, 1365-8050
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Popis
Shrnutí: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 $m^2$ 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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.12709