{"paper":{"title":"Degrees and Gaps: Tight Complexity Results of General Factor Problems Parameterized by Treewidth and Cutwidth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"D\\'aniel Marx, Govind S. Sankar, Philipp Schepper","submitted_at":"2021-05-19T08:26:18Z","abstract_excerpt":"For the General Factor problem we are given an undirected graph $G$ and for each vertex $v\\in V(G)$ a finite set $B_v$ of non-negative integers. The task is to decide if there is a subset $S\\subseteq E(G)$ such that $deg_S(v)\\in B_v$ for all vertices $v$ of $G$. The maxgap of a finite integer set $B$ is the largest $d\\ge 0$ such that there is an $a\\ge 0$ with $[a,a+d+1]\\cap B=\\{a,a+d+1\\}$. Cornu\\'ejols (1988) showed that if the maxgap of all sets $B_v$ is at most 1, then the decision version of General Factor is poly-time solvable. Dudycz and Paluch (2018) extended this result for the minimiza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08980","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.08980/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}