点着色图的热带控制集
Tropical Dominating Sets in Vertex-Coloured Graphs
摘要：
给定一个顶点着色图，如果图的每一种颜色在一个支配集中至少出现一次，则称该配集是热带的。在这里，我们研究最小热带控制集的结构和算法的观点。首先，我们证明了热带支配集问题即使在简单路的情况下也是NP-完全的，然后，我们建立了与图的各种参数如最小度和边数有关的上界.我们还给出了随机图的上界。最后，我们给出了一般图类和限制图类的可逼近性和不可逼近性结果，并建立了区间图的FPT算法。
英文摘要：
Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various parameters of the graph such as minimum degree and number of edges. We also give upper bounds for random graphs. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
