Research confirms the burning conjecture for 3-caterpillars and 4-caterpillars, suggesting broader implications.
The burning number [Formula: see text] of a graph [Formula: see text], introduced by Bonato, is the minimum number of steps to burn the graph. Bonato et al. (2014) conjectured that [Formula: see text] for any connected graph [Formula: see text] of order [Formula: see text]. In this paper, we confirmed this conjecture for 3-caterpillars and 4-caterpillars and then bounded the burning number of [Formula: see text]-caterpillars.
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Y et al. (2026) studied this question.
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