{"paper":{"title":"Towards a Characterization of Leaf Powers by Clique Arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Christian Rosenke, Ragnar Nevries","submitted_at":"2014-02-06T17:35:18Z","abstract_excerpt":"The class ${\\cal L}_k$ of $k$-leaf powers consists of graphs $G=(V,E)$ that have a $k$-leaf root, that is, a tree $T$ with leaf set $V$, where $xy \\in E$, if and only if the $T$-distance between $x$ and $y$ is at most $k$. Structure and linear time recognition algorithms have been found for $2$-, $3$-, $4$-, and, to some extent, $5$-leaf powers, and it is known that the union of all $k$-leaf powers, that is, the graph class ${\\cal L} = \\bigcup_{k=2}^\\infty {\\cal L}_k$, forms a proper subclass of strongly chordal graphs. Despite from that, no essential progress has been made lately. In this pap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1425","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"}