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An $H$-path of $D$ is a path $(v_0, \\dots, v_n)$ of $D$ such that $(c(v_{i-1}, v_i), c(v_i,v_{i+1}))$ is an arc of $H$ for every $1 \\le i \\le n-1$. For $u, v \\in V_D$, we say that $u$ reaches $v$ by $H$-paths if there exists an $H$-path from $u$ to $v$ in $D$. A subset $S \\subseteq V_D$ is $H$-absorbent of $D$ if every vertex in $V_D-S$ reaches by $H$-paths some vertex in $S$, and it is $H$-independent if no vertex in $S$ can reach anothe"},"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":"1903.10031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-24T18:06:03Z","cross_cats_sorted":[],"title_canon_sha256":"bcfc258f104e261a9f10bef2a8f0a3af7c568bfb97aaaa2c2e70b7593bd98bcb","abstract_canon_sha256":"c20b1a7416f826f25968e771acaf89261137069c4aab6a77459081014a6200ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:34.729206Z","signature_b64":"Vu3OnheBhTVaXuInHYK+NlwWwSJR71LRCLZ9O1rcWAyBM39s1KXbrDQD5e/2Ic3z42gXUexwrqLjg7iVubnTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eab3428c3f150565d047432299c952cc522790160bc5c266b0ae84ad36c1b3ee","last_reissued_at":"2026-05-17T23:50:34.728587Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:34.728587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Panchromatic patterns by paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C\\'esar Hern\\'andez-Cruz, Germ\\'an Ben\\'itez-Bobadilla, Hortensia Galeana-S\\'anchez","submitted_at":"2019-03-24T18:06:03Z","abstract_excerpt":"Let $H=(V_H,A_H)$ be a digraph, possibly with loops, and let $D=(V_D, A_D)$ be a loopless multidigraph with a colouring of its arcs $c: A_D \\rightarrow V_H$. An $H$-path of $D$ is a path $(v_0, \\dots, v_n)$ of $D$ such that $(c(v_{i-1}, v_i), c(v_i,v_{i+1}))$ is an arc of $H$ for every $1 \\le i \\le n-1$. For $u, v \\in V_D$, we say that $u$ reaches $v$ by $H$-paths if there exists an $H$-path from $u$ to $v$ in $D$. 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