{"paper":{"title":"Revisiting the Hamiltonian Theme in the Square of a Block: The General Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gek L. Chia, Herbert Fleischner","submitted_at":"2018-05-11T13:10:43Z","abstract_excerpt":"This is the second part of joint research in which we show that every $2$-connected graph $G$ has the ${\\cal F}_4$ property. That is, given distinct $x_i\\in V(G)$, $1\\leq i\\leq 4$, there is an $x_1x_2$-hamiltonian path in $G^2$ containing different edges $x_3y_3, x_4y_4\\in E(G)$ for some $y_3,y_4\\in V(G)$. However, it was shown already in \\cite[Theorem 2]{cf1:refer} that 2-connected DT-graphs have the ${\\cal F}_4$ property; based on this result we generalize it to arbitrary $2$-connected graphs. We also show that these results are best possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04378","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"}