{"paper":{"title":"About $(k,l)$-kernels, semikernels and Grundy functions in partial line digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Camino Balbuena, Hortensia Galeana-S\\'anchez, Mukuy-kak Guevara","submitted_at":"2016-01-28T14:41:00Z","abstract_excerpt":"Let $D=(V,A)$ be a digraph and consider an arc subset $A'\\subseteq A$ and an exhaustive mapping $\\phi: A\\to A'$ such that\n  $(i)$ the set of heads of $A'$ is $H(A')=V$; $(ii)$ the map fixes the elements of $A'$, that is, $\\phi|A'=Id$, and for every vertex $j\\in V$, $\\phi(\\omega^-(j))\\subset \\omega^-(j)\\cap A'$.\n  Then, {\\it the partial line digraph} of $D$, denoted by $\\mathcal{L}_{(A',\\phi)}D $ (for short $\\mathcal{L}D$ if the pair $(A', \\phi)$ is clear from the context), is the digraph with vertex set $V (\\mathcal{L}D)=A'$ and set of arcs $A(\\mathcal{L}D) = \\{(ij, \\phi(j,k)) : (j,k)\\in A\\}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07775","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"}