{"paper":{"title":"Packing Coloring of Undirected and Oriented Generalized Theta Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Daouya La\\\"iche (L'IFORCE), Eric Sopena (LaBRI), Isma Bouchemakh (L'IFORCE)","submitted_at":"2016-06-03T14:36:26Z","abstract_excerpt":"The packing chromatic number $\\chi$ $\\rho$ (G) of an undirected (resp. oriented) graph G is the smallest integer k such that its set of vertices V (G) can be partitioned into k disjoint subsets V 1,..., V k, in such a way that every two distinct vertices in V i are at distance (resp. directed distance) greater than i in G for every i, 1 $\\le$ i $\\le$ k. The generalized theta graph $\\Theta$ {\\ell} 1,...,{\\ell}p consists in two end-vertices joined by p $\\ge$ 2 internally vertex-disjoint paths with respective lengths 1 $\\le$ {\\ell} 1 $\\le$ . . .  $\\le$ {\\ell} p. We prove that the packing chromati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01107","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"}