广义图搜索树
Generalized Graph Search Trees
- Brandenburg University of Technology（勃兰登堡工业大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文推广图搜索树概念，允许任意先前邻居作为父节点，研究其识别问题的复杂性，证明多数搜索为NP完全，并在二分图与弦图上给出多项式时间算法。
AI中文摘要：
图搜索算法及其对应的图搜索树在算法图论中被广泛使用。近年来，这些图搜索树的识别问题受到了极大的关注。到目前为止，研究主要集中在两类搜索树上：行为类似于BFS树的首入树和类似于DFS树的末入树。这两种搜索树范式之间的区别在于顶点所连接的父节点不同。在首入树中，父节点是第一个被访问的邻居；而在末入树中，父节点是该顶点之前最后被访问的邻居。在此，我们将通过允许顶点的任意一个先前访问的邻居作为父节点来推广这些图搜索树的概念。我们研究了这些广义图搜索树的识别问题的复杂性。我们为大多数搜索给出了NP完全性证明。我们还表明，该问题对于通用搜索是平凡的，并且在二分图和弦图上对于若干搜索可以在多项式时间内求解。我们还研究了固定起始顶点如何影响问题复杂性这一问题。
英文摘要：
Graph search algorithms and their corresponding graph search trees are commonly used in algorithmic graph theory. In recent years, the recognition problem of these graph search trees has received significant attention. So far, the research has focused on two types of search trees: first-in trees that behave like BFS-trees and last-in trees that behave like DFS-trees. The search tree paradigms differ from each other by the parent a vertex is connected to. In first-in trees, it is the first visited neighbor, while in last-in trees it is the last neighbor visited before that vertex. Here, we will generalize these concepts of graph search trees by allowing every preceding neighbor of a vertex to be the parent. We study the complexity of the recognition problem of these generalized graph search trees. We present NP-completeness proofs for most searches. We also show that the problem is trivial for Generic Search and polynomial-time solvable for several searches on bipartite graphs and chordal graphs. We also study the question how fixing the start vertex influences the complexity of the problem.
