Graph Burning On Large $p$-Caterpillars
Danielle Cox, M.E. Messinger, Kerry Ojakian

TL;DR
This paper proves the burning number conjecture for large $p$-caterpillars, a class of tree-like graphs, advancing understanding of information spread models in graph theory.
Contribution
It establishes the conjecture for a new class of graphs, large $p$-caterpillars, extending previous partial results.
Findings
Burning number conjecture holds for sufficiently large $p$-caterpillars.
Provides new bounds and techniques for analyzing graph burning.
Enhances understanding of contagion spread in complex tree structures.
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 vertices, all vertices can be burned after at most 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 -caterpillars.
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Taxonomy
TopicsAdvanced Graph Theory Research · Data Management and Algorithms · Graph Labeling and Dimension Problems
