{"paper":{"title":"On Hamilton Decompositions of Line Graphs of Non-Hamiltonian Graphs and Graphs without Separating Transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Barbara Maenhaut, Benjamin R. Smith, Darryn Bryant","submitted_at":"2017-10-17T00:27:14Z","abstract_excerpt":"In contrast with Kotzig's result that the line graph of a $3$-regular graph $X$ is Hamilton decomposable if and only if $X$ is Hamiltonian, we show that for each integer $k\\geq 4$ there exists a simple non-Hamiltonian $k$-regular graph whose line graph has a Hamilton decomposition. We also answer a question of Jackson by showing that for each integer $k\\geq 3$ there exists a simple connected $k$-regular graph with no separating transitions whose line graph has no Hamilton decomposition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06037","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"}