燃烧杠铃的数量

Pub Date : 2024-03-27 DOI:10.1007/s10255-024-1113-8

Hui-qing Liu, Rui-ting Zhang, Xiao-lan Hu

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引用次数: 0

摘要

图 G 的燃烧数 b(G)定义为：对于图 G 的每个顶点 u，存在 i∈ {1,...,k}，且 dG(u,xi)≤k-i，以及 dG(xi,xj)≥j-i（对于任意 1≤i <j≤k）的最小整数 k，对于该整数，存在顶点 x1,...,xk，且对于图 G 的每个顶点 u，存在 i∈ {1,...,k}，且 dG(u,xi)≤k-i。即使对于某些最大阶数为三的无循环图，图燃烧问题也被证明是 NP-完全的。在本文中，我们将分别确定所有短杠铃和长杠铃的燃烧数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Burning Numbers of Barbells

Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph, the burning number b(G) of a graph G, is defined as the smallest integer k for which there are vertices x₁,…,x_k such that for every vertex u of G, there exists i ∈ {1,…,k} with d_G(u, x_i) ≤ k − i, and d_G(x_i, x_j) ≥ j − i for any 1 ≤ i < j ≤ k. The graph burning problem has been shown to be NP-complete even for some acyclic graphs with maximum degree three. In this paper, we determine the burning numbers of all short barbells and long barbells, respectively.

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