{"paper":{"title":"Blocker size via matching minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nikola Yolov","submitted_at":"2016-06-20T19:32:18Z","abstract_excerpt":"Finding the maximum number of maximal independent sets in an $n$-vertex graph $G$, $i(G)$, from a restricted class is an extensively studied problem. Let $kK_2$ denote the matching of size $k$, that is a graph with $2k$ vertices and $k$ disjoint edges. A graph with an induced copy of $kK_2$ contains at least $2^k$ maximal independent sets. The other direction was established in a series of papers finally yielding $i(G) \\le (n/k)^{2k}$ for a graph $G$ without an induced $(k+1)K_2$. Alekseev proved that $i(G)$ is at most the number of induced matchings of $G$.\n  This work generalises the aforeme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06263","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"}