Abstract
We study the geodesic complexity of the ordered and unordered configuration spaces of graphs in both the and metrics. We determine the geodesic complexity of the ordered two-point –configuration space of any star graph in both the and metrics and of the unordered two-point configuration space of any tree in the metric, by finding explicit geodesics from any pair to any other pair, and arranging them into a minimal number of continuously varying families. In each case the geodesic complexity matches the known value of the topological complexity.
Citation
Donald M Davis. Michael Harrison. David Recio-Mitter. "Two robots moving geodesically on a tree." Algebr. Geom. Topol. 22 (2) 785 - 814, 2022. https://doi.org/10.2140/agt.2022.22.785
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