Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static graphs, which often stand in contrast to practice where data is inherently dynamic. A temporal graph has an edge set that changes over time. We present a natural temporal extension of the classical graph coloring problem. Given a temporal graph and integers k and Δ, we ask for a coloring sequence with at most k colors for each vertex such that in every time window of Δ consecutive time steps, in which an edge is present, this edge is properly colored at least once. We thoroughly investigate the computational complexity of this temporal coloring problem. More specifically, we prove strong computational hardness results, complemented by efficient exact and approximation algorithms.

图形着色是在计划和调度，资源分配和模式匹配等广泛领域中应用的最著名的计算问题之一。到目前为止，着色问题主要在静态图上进行研究，而静态图通常与数据固有动态的实践形成对比。时间图具有随时间变化的边集。我们提出了经典图着色问题的自然时间扩展。给定一个时间图以及整数k和Δ，我们要求着色序列最多为k为每个顶点着色，以使在Δ个连续时间步长的每个时间窗口（其中存在边缘）中，该边缘至少被正确着色一次。我们彻底研究了此时间着色问题的计算复杂性。更具体地说，我们证明了强大的计算硬度结果，并辅之以高效的精确算法和近似算法。