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arXiv · 1810.09974

Algorithmic Traversals of Infinite Graphs

Siddharth Bhaskar·Anton Jay Kienzle
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Abstract

A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various graph searching algorithms. We extend the theory of generic search and breadth-first search from finite graphs to wellordered infinite graphs, recovering the notion of "search trees" in this context. We also prove tight upper bounds on the extent to which graph search and breadth-first search can modify the order type of the original graph, as well as characterize the traversals computed by these algorithms as lexicographically minimal.

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Siddharth Bhaskar, Anton Jay Kienzle. 2018-10-23. Algorithmic Traversals of Infinite Graphs. https://arxiv.org/abs/1810.09974

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