Burnability of double spiders and path forests

• Discrete-time deterministic graph algorithm modelling the spread of social contagion. Tight bounds on burning numbers double spiders and path forests. Well-burnability forests with sufficiently long paths. Progress towards a conjecture stronger than number conjecture. The can be used to measure spreading speed contagion in network. is arguably main unresolved related this parameter, which settled by showing that every tree order m 2 has at most . This known hold for many classes trees, including - trees exactly one vertex degree greater two. In fact, it been verified certain slightly larger also have , result then conjectured true all trees. first focus paper verify two vertices degrees least three they are adjacent. Our other concerns forests, class graphs their naturally spiders. Here, our shows forest shortest smallest possible any same order.