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Note for the Burning Conjecture on p-Caterpillars | Synapse

May 8, 2026

Note for the Burning Conjecture on p-Caterpillars

Key Points

The aim is to verify the burning conjecture for specific types of graphs, namely p-caterpillars.
Confirmed burning conjecture for 3-caterpillars and 4-caterpillars.
Established bounds for the burning number of p-caterpillars.
Confirmed conjecture holds for 3-caterpillars with an adequate burning number.
Verified that 4-caterpillars also satisfy the conjectured bounds.
Provided new bounds for the burning number of p-caterpillars.

Abstract

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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Authors

L

Li Y

G

Guiyu Shi

J

Jiaqing Wu

Journals

Journal of Interconnection Networks

Actions

Institutions

Qinghai University for Nationalities

References and Citations

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Cite this study

Y et al. (Wed,) studied this question.

www.synapsesocial.com/papers/69fd7eb0bfa21ec5bbf06fcc — DOI: https://doi.org/10.1142/s0219265926500106