The Burning Number Conjecture for trees
Let be a tree on vertices, and let denote its burning number.
Tree form of the Burning Number Conjecture. Every tree on vertices satisfies
Since every connected graph has a spanning tree and deleting edges cannot decrease the burning number, this is sufficient to prove the Burning Number Conjecture. The assertion is established for several subclasses of trees, but remains open for general trees.
References
Primary source
John Peca-Medlin, “Burning rooted graph products”, arXiv:2603.00304 (2026).
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