{"paper":{"title":"Contraction and Deletion Blockers for Perfect Graphs and $H$-free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Bernard Ries, Christophe Picouleau, Dani\\\"el Paulusma, \\\"Oznur Ya\\c{s}ar Diner","submitted_at":"2017-06-27T21:16:25Z","abstract_excerpt":"We study the following problem: for given integers $d$, $k$ and graph $G$, can we reduce some fixed graph parameter $\\pi$ of $G$ by at least $d$ via at most $k$ graph operations from some fixed set $S$? As parameters we take the chromatic number $\\chi$, clique number $\\omega$ and independence number $\\alpha$, and as operations we choose the edge contraction ec and vertex deletion vd. We determine the complexity of this problem for $S=\\{\\mbox{ec}\\}$ and $S=\\{\\mbox{vd}\\}$ and $\\pi\\in \\{\\chi,\\omega,\\alpha\\}$ for a number of subclasses of perfect graphs. We use these results to determine the compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09052","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"}