{"paper":{"title":"On the Computational Complexity of the Bipartizing Matching Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Carlos V.G.C. Lima, Dieter Rautenbach, Jayme L. Szwarcfiter, U\\'everton S. Souza","submitted_at":"2017-10-21T02:25:50Z","abstract_excerpt":"We study the problem of determining whether a given graph~$G=(V,E)$ admits a matching~$M$ whose removal destroys all odd cycles of~$G$ (or equivalently whether~$G-M$ is bipartite). This problem is equivalent to determine whether~$G$ admits a~$(2,1)$-coloring, which is a~$2$-coloring of~$V(G)$ such that each color class induces a graph of maximum degree at most~$1$. We determine a dichotomy related to the~{\\sf NP}-completeness of this problem, where we show that it is~{\\sf NP}-complete even for $3$-colorable planar graphs of maximum degree~$4$, while it is known that the problem can be solved i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07741","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"}