{"paper":{"title":"A Note on Signed k-Submatching in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"K. Ehsani, M. Dalirrooyfard, R. Sherkati, S. Akbari","submitted_at":"2014-11-01T16:12:33Z","abstract_excerpt":"Let $G$ be a graph of order $n$. For every $v\\in V(G)$, let $E_G(v)$ denote the set of all edges incident with $v$. A signed $k$-submatching of $G$ is a function $f:E(G)\\longrightarrow \\{-1,1\\}$, satisfying $f(E_G(v))\\leq 1$ for at least $k$ vertices, where $f(S)=\\sum_{e\\in S}f(e)$, for each $ S\\subseteq E(G)$. The maximum of the value of $f(E(G))$, taken over all signed $k$-submatching $f$ of $G$, is called the signed $k$-submatching number and is denoted by $\\beta ^k_S(G)$. In this paper, we prove that for every graph $G$ of order $n$ and for any positive integer $k \\leq n$, $\\beta ^k_S (G) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0132","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"}