Graph Burning On Large $p$-Caterpillars

Danielle Cox; M. E. Messinger; Kerry Ojakian

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arXiv · 2412.12970

Graph Burning On Large $p$-Caterpillars

Danielle Cox·M. E. Messinger·Kerry Ojakian

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Abstract

Graph burning models the spread of information or contagion in a graph. At each time step, two events occur: neighbours of already burned vertices become burned, and a new vertex is chosen to be burned. The big conjecture is known as the {\it burning number conjecture}: for any connected graph on $n$ vertices, all $n$ vertices can be burned after at most $\lceil \sqrt{n}\ \rceil$ time steps. It is well-known that to prove the conjecture, it suffices to prove it for trees. We prove the conjecture for sufficiently large $p$-caterpillars.

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BibTeX RIS

Danielle Cox, M. E. Messinger, Kerry Ojakian. 2024-12-17. Graph Burning On Large $p$-Caterpillars. https://arxiv.org/abs/2412.12970

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