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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.01107","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-06-03T14:36:26Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"de3e8e7a62e6b291a41ea4660c7d168d58076087a69c543039e8735bfb8c08e0","abstract_canon_sha256":"92e423db9ff67e7016922bf865c0dd127449db824e692d959105b15e114f1749"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:27.559645Z","signature_b64":"6wt/IdeiauthrPsCyBvzDjQbZm4Uxux4vTTMc+ZEiSyWpJhUfoUJNlzv6LEeOjMIbDAfByV5g3bmL5XIdlWpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f52f1110ff7451192045241f71401ef13da00343a3546fc6bc71beb7d710304","last_reissued_at":"2026-05-18T01:04:27.558908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:27.558908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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