{"paper":{"title":"Signless Laplacian spectral radius and fractional matchings in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ruifang Liu, Yu Lu","submitted_at":"2017-11-07T06:55:54Z","abstract_excerpt":"A {\\it fractional matching} of a graph $G$ is a function $f$ giving each edge a number in $[0,1]$ so that $\\sum_{e\\in \\Gamma(v)}f(e)\\leq 1$ for each $v\\in V(G)$, where $\\Gamma(v)$ is the set of edges incident to $v$. The {\\it fractional matching number} of $G$, written $\\alpha'_{*}(G)$, is the maximum of $\\sum_{e\\in E(G)}f(e)$ over all fractional matchings $f$. In this paper, we propose the relations between the fractional matching number and the signless Laplacian spectral radius of a graph. As applications, we also give sufficient spectral conditions for existence of a fractional perfect mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02310","kind":"arxiv","version":2},"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"}