{"paper":{"title":"Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Christian Komusiewicz, Erik Jan van Leeuwen, Iyad Kanj, Manuel Sorge","submitted_at":"2017-02-14T18:21:28Z","abstract_excerpt":"A graph $G$ is a $(\\Pi_A,\\Pi_B)$-graph if $V(G)$ can be bipartitioned into $A$ and $B$ such that $G[A]$ satisfies property $\\Pi_A$ and $G[B]$ satisfies property $\\Pi_B$. The $(\\Pi_{A},\\Pi_{B})$-Recognition problem is to recognize whether a given graph is a $(\\Pi_A,\\Pi_B)$-graph. There are many $(\\Pi_{A},\\Pi_{B})$-Recognition problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of $(\\Pi_A,\\Pi_B)$-Recognition based on a technique which we dub inductive recognition. In particular, we give fixed-parameter algorithms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04322","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"}