{"paper":{"title":"Strong geodetic problem in grid like architectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Paul Manuel, Sandi Klav\\v{z}ar","submitted_at":"2017-08-13T07:45:13Z","abstract_excerpt":"A recent variation of the classical geodetic problem, the strong geodetic problem, is defined as follows. If $G$ is a graph, then ${\\rm sg}(G)$ is the cardinality of a smallest vertex subset $S$, such that one can assign a fixed geodesic to each pair $\\{x,y\\}\\subseteq S$ so that these $\\binom{|S|}{2}$ geodesics cover all the vertices of $G$. In this paper, the strong geodesic problem is studied on Cartesian product graphs. A general upper bound is proved on the Cartesian product of a path with an arbitrary graph and showed that the bound is tight on flat grids and flat cylinders."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03869","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}