有向图的燃烧数：界与计算复杂性
The Burning Number of Directed Graphs: Bounds and Computational Complexity
摘要：
图的燃烧数是最近由Bonato等人提出的，虽然他们提到燃烧数可以自然地推广到有向图，但没有进一步的研究。在这里，我们介绍了有向图的燃烧，我们研究了相应的燃烧数的界限和找到这个数字的难度。我们从简单的算法和例子中推导出清晰的界限。难度问题产生了更令人惊讶的结果：寻找有向树的燃烧数是NP困难的，但FPT;然而，对于DAGs来说，它是W[2]-完全的。最后，我们给出了一个固定参数的算法来寻找燃烧数的有向图，与一个参数的启发，在系统发育网络的研究。
英文摘要：
The burning number of a graph was recently introduced by Bonato et al. Although they mention that the burning number generalises naturally to directed graphs, no further research on this has been done. Here, we introduce graph burning for directed graphs, and we study bounds for the corresponding burning number and the hardness of finding this number. We derive sharp bounds from simple algorithms and examples. The hardness question yields more surprising results: finding the burning number of a directed tree is NP-hard, but FPT; however, it is W[2]-complete for DAGs. Finally, we give a fixed-parameter algorithm to find the burning number of a digraph, with a parameter inspired by research in phylogenetic networks.
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