{"paper":{"title":"On bipartization of cubic graphs by removal of an independent set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Hanna Furma\\'nczyk, Marek Kubale, Stanis{\\l}aw Radziszowski","submitted_at":"2014-06-10T21:45:03Z","abstract_excerpt":"We study a new problem for cubic graphs: bipartization of a cubic graph $Q$ by deleting sufficiently large independent set $I$. It can be expressed as follows: \\emph{Given a connected $n$-vertex tripartite cubic graph $Q=(V,E)$ with independence number $\\alpha(Q)$, does $Q$ contain an independent set $I$ of size $k$ such that $Q-I$ is bipartite?} We are interested for which value of $k$ the answer to this question is affirmative. We prove constructively that if $\\alpha(Q) \\geq 4n/10$, then the answer is positive for each $k$ fulfilling $\\lfloor (n-\\alpha(Q))/2 \\rfloor \\leq k \\leq \\alpha(Q)$. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2728","kind":"arxiv","version":2},"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"}