Geodesic
A Note on Graph Burning of Path Forests
Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 3.

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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.
DOI : 10.46298/dmtcs.12709
Classification : 05A17, 05C85, 68R10 
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Tan, Ta Sheng; Teh, Wen Chean. A Note on Graph Burning of Path Forests. Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 3. doi : 10.46298/dmtcs.12709. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12709/

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