{"paper":{"title":"Leaf realization problem, caterpillar graphs and prefix normal words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alain Goupil, Alexandre Blondin Mass\\'e, \\'Elise Vandomme, \\'Emile Nadeau, Julien de Carufel, M\\'elodie Lapointe","submitted_at":"2017-12-05T21:53:30Z","abstract_excerpt":"Given a simple graph $G$ with $n$ vertices and a natural number $i \\leq n$, let $L_G(i)$ be the maximum number of leaves that can be realized by an induced subtree $T$ of $G$ with $i$ vertices. We introduce a problem that we call the \\emph{leaf realization problem}, which consists in deciding whether, for a given sequence of $n+1$ natural numbers $(\\ell_0, \\ell_1, \\ldots, \\ell_n)$, there exists a simple graph $G$ with $n$ vertices such that $\\ell_i = L_G(i)$ for $i = 0, 1, \\ldots, n$. We present basic observations on the structure of these sequences for general graphs and trees. In the particu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01942","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"}