{"paper":{"title":"Counting Hamiltonian paths between prescribed vertices in traceable graphs with a forbidden induced subgraph","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carol T. Zamfirescu, Jorik Jooken","submitted_at":"2026-06-01T14:03:31Z","abstract_excerpt":"For graphs $G$ and $F$, we say that $G$ is $F$-free if $F$ does not occur as an induced subgraph of $G$. This paper is concerned with the following question: Given an $F$-free graph $G$ having two vertices between which there exists at least one Hamiltonian path, how many Hamiltonian paths between these endpoints must exist (in terms of the order of $G$)? Our main result shows that there exists a sharp dichotomy. More precisely, we show that if $F$ is not an induced subgraph of $P_3+sP_1$ for any integer $s \\geq 0$, then there exists an infinite family of $F$-free graphs having two vertices be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02279","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.02279/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}