{"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 $D$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10031","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"}