We study here the problem of exploring a temporal graph when the underlying graph is a star. The aim of the exploration problem in a temporal star is finding a temporal walk which starts and finishes at the center of the star, and visits all leaves. We present a systematic study of the computational complexity of this problem, depending on the number k of time points where each edge can be present in the graph. We distinguish between the decision version StarExp(k), asking whether a complete exploration exists, and the maximization version MaxStarExp(k), asking for an exploration of the greatest possible number of edges. We fully characterize MaxStarExp(k) in terms of complexity. We also partially characterize StarExp(k), showing that it is in P for $k<4$, but is NP-complete, for every $k>5$. Finally, we partially characterize classes of “random” temporal stars which are, asymptotically almost surely, yes-instances and no-instances for StarExp(k).

我们在这里研究当基础图是星形时探索时间图的问题。在时空恒星中探索问题的目的是找到在恒星中心开始和结束并拜访所有叶子的时空行走。我们根据该图中每个边都可以出现的时间点的数量k，对这个问题的计算复杂性进行了系统的研究。我们区分询问版本是否存在完整探索的决策版本StarExp（k ）和询问最大可能数目的边的最大化版本MaxStarExp（k ）。我们充分表征了MaxStarExp（k ）就复杂性而言。我们还部分表征了StarExp（k ），表明它在P中表示$ķ<4$，但对每个人来说NP都是完整的 $ķ>5$。最后，我们部分地表征了“随机”时态恒星的类，这些恒星几乎渐近地肯定是StarExp（k ）的yes-instance和no-instance 。