{"paper":{"title":"Pseudo and Strongly Pseudo 2--Factor Isomorphic Regular Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. Labbate, J. Sheehan, M. Abreu","submitted_at":"2010-02-04T16:26:48Z","abstract_excerpt":"A graph $G$ is pseudo 2--factor isomorphic if the parity of the number of cycles in a 2--factor is the same for all 2--factors of $G$. In \\cite{ADJLS} we proved that pseudo 2--factor isomorphic $k$--regular bipartite graphs exist only for $k \\le 3$. In this paper we generalize this result for regular graphs which are not necessarily bipartite. We also introduce strongly pseudo 2--factor isomorphic graphs and we prove that pseudo and strongly pseudo 2--factor isomorphic 2k--regular graphs and $k$--regular digraphs do not exist for $k\\geq 4$. Moreover, we present constructions of infinite famili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1033","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"}