{"paper":{"title":"Induced Matchings in Graphs of Maximum Degree 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Joos","submitted_at":"2014-07-31T10:01:50Z","abstract_excerpt":"For a graph $G$, let $\\nu_s(G)$ be the induced matching number of $G$. We prove the sharp bound $\\nu_s(G)\\geq \\frac{n(G)}{9}$ for every graph $G$ of maximum degree at most $4$ and without isolated vertices that does not contain a certain blown up $5$-cycle as a component. This result implies a consequence of the well known conjecture of Erd\\H{o}s and Ne\\v{s}et\\v{r}il, saying that the strong chromatic index $\\chi_s'(G)$ of a graph $G$ is at most $\\frac{5}{4}\\Delta(G)^2$, because $\\nu_s(G)\\geq \\frac{m(G)}{\\chi_s'(G)}$ and $n(G)\\geq \\frac{m(G)\\Delta(G)}{2}$. Furthermore, it is shown that there is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8336","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"}