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This notion generalizes that of semicomplete digraphs which are $0$-semicomplete and tournaments which are semicomplete and have no anti-parallel pairs of edges. Our results in this paper are as follows. (1) We give an algorithm which, given an $h$-semicomplete digraph $G$ on $n$ vertices and a positive integer $k$, in $(h + 2k + 1)^{2k} n^{O(1)}$ time either construc"},"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":"1507.01934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-07T19:55:36Z","cross_cats_sorted":[],"title_canon_sha256":"92efa9ebb78373794dd3d978fc64b3548907e1b7b810e627249e84acc20dda41","abstract_canon_sha256":"7b8dd572b3e7c22eaeaec9e92172f4237d8a7850a66f86ce6a60583292a4a78b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:11.964276Z","signature_b64":"CjrqXuRy7ENT7xRNEuDBT7UsLVLuYOU7mQVnL8nXoaF+zpnew/XpRn+6Y0WD/yPEKnb6IN41o9MoAi0Mp0TCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"057d3c97905163ca3716cdb7416f7599975dee08a46415899c8907f5c7b0dec0","last_reissued_at":"2026-05-18T01:37:11.963415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:11.963415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the pathwidth of almost semicomplete digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hisao Tamaki, Kenta Kitsunai, Yasuaki Kobayashi","submitted_at":"2015-07-07T19:55:36Z","abstract_excerpt":"We call a digraph {\\em $h$-semicomplete} if each vertex of the digraph has at most $h$ non-neighbors, where a non-neighbor of a vertex $v$ is a vertex $u \\neq v$ such that there is no edge between $u$ and $v$ in either direction. 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