{"paper":{"title":"Erd\\H{o}s-Ko-Rado Theorems for a Family of Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carl Feghali, Daniel Thomas, Matthew Johnson","submitted_at":"2015-06-25T13:21:14Z","abstract_excerpt":"Given a graph $G$ and an integer $r\\geq 1$, let $\\mathcal{I}^{(r)}(G)$ denote the family of independent sets of size $r$ of $G$. For a vertex $v$ of $G$, let $\\mathcal{I}^{(r)}_v(G)$ denote the family of independent sets of size $r$ that contain~$v$. This family is called an $r$-star and $v$ is the centre of the star. Then $G$ is said to be $r$-EKR if no pairwise intersecting subfamily of $\\mathcal{I}^{(r)}(G)$ is bigger than the largest $r$-star, and if every maximum size pairwise intersecting subfamily of $\\mathcal{I}^{(r)}(G)$ is an $r$-star, then $G$ is said to be strictly $r$-EKR. Let $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07741","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"}