{"paper":{"title":"On random trees obtained from permutation graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huseyin Acan, Pawel Hitczenko","submitted_at":"2014-06-16T10:29:08Z","abstract_excerpt":"A permutation $\\boldsymbol w$ gives rise to a graph $G_{\\boldsymbol w}$; the vertices of $G_{\\boldsymbol w}$ are the letters in the permutation and the edges of $G_{\\boldsymbol w}$ are the inversions of $\\boldsymbol w$. We find that the number of trees among permutation graphs with $n$ vertices is $2^{n-2}$ for $n\\ge 2$. We then study $T_n$, a uniformly random tree from this set of trees. In particular, we study the number of vertices of a given degree in $T_n$, the maximum degree in $T_n$, the diameter of $T_n$, and the domination number of $T_n$. Denoting the number of degree-$k$ vertices in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3958","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"}