{"paper":{"title":"On an Annihilation Number Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Eugen Mandrescu, Vadim E. Levit","submitted_at":"2018-11-12T13:40:45Z","abstract_excerpt":"Let $\\alpha(G)$ denote the cardinality of a maximum independent set, while $\\mu(G)$ be the size of a maximum matching in the graph $G=\\left(V,E\\right) $. If $\\alpha(G)+\\mu(G)=\\left\\vert V\\right\\vert $, then $G$ is a K\\\"onig-Egerv\\'ary graph. If $d_{1}\\leq d_{2}\\leq\\cdots\\leq d_{n}$ is the degree sequence of $G$, then the annihilation number $h\\left(G\\right) $ of $G$ is the largest integer $k$ such that $\\sum\\limits_{i=1}^{k}d_{i}\\leq\\left\\vert E\\right\\vert $ (Pepper 2004, Pepper 2009). A set $A\\subseteq V$ satisfying $\\sum \\limits_{a\\in A} deg(a)\\leq\\left\\vert E\\right\\vert $ is an annihilation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04722","kind":"arxiv","version":3},"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"}