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Every connected graph G with twin cover X of size t satisfies χ(G) ≤ svcfc(G) ≤ χ(G) + t."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The kernelization result assumes a twin cover X is supplied as part of the input; the FPT claim for tc(G) + k therefore depends on either the cover being given or on the complexity of computing it separately."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Kernelization establishes FPT for strong CFVC number by twin cover plus k, with svcfc(G) bounded between χ(G) and χ(G) plus twin cover size."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A graph with twin cover of size t has strong conflict-free vertex-connection number at most its chromatic number plus t."}],"snapshot_sha256":"5b766251d78386c90c3028ae89282a95889195e111b68e4bfd27fec2f999fcf3"},"formal_canon":{"evidence_count":1,"snapshot_sha256":"b48e3de948d75832b114bc363b10a8cfaad3c0a185d1a37bc738b4f47f624648"},"paper":{"abstract_excerpt":"A vertex-coloring of a connected graph $G$ is a strong conflict-free vertex-connection coloring if every two distinct vertices are joined by a shortest path on which some color appears exactly once. The minimum number of colors in such a coloring is the strong conflict-free vertex-connection number $\\operatorname{svcfc}(G)$. We study this problem under the parameter twin cover.\n  Let $X$ be a twin cover of $G$ of size $t$, and let $k$ be the target number of colors. In our first result, given $(G,k)$ together with a twin cover $X$, we reduce in polynomial time to an equivalent annotated instan","authors_text":"Samuel German","cross_cats":["cs.DS"],"headline":"A graph with twin cover of size t has strong conflict-free vertex-connection number at most its chromatic number plus t.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2026-05-13T10:13:01Z","title":"Strong Conflict-Free Vertex-Connection via Twin Cover: Kernelization and Chromatic Bounds"},"references":{"count":11,"internal_anchors":0,"resolved_work":11,"sample":[{"cited_arxiv_id":"","doi":"10.1016/j.dam.2024.03.021","is_internal_anchor":false,"ref_index":1,"title":"Discrete Applied Mathematics352, 88–104 (2024)","work_id":"7512394d-3307-4727-b596-0b1f2d9dfbab","year":2024},{"cited_arxiv_id":"","doi":"10.7151/dmgt.2036","is_internal_anchor":false,"ref_index":2,"title":"Discussiones Mathematicae Graph Theory38(4), 911–920 (2018)","work_id":"80096e22-90d9-44fe-bd92-681d0555cdd0","year":2018},{"cited_arxiv_id":"","doi":"10.1137/s0097539702431840","is_internal_anchor":false,"ref_index":3,"title":"SIAM Journal on Computing33(1), 94–136 (2003)","work_id":"0895d1b1-b83f-4305-9bb9-ccab69387e97","year":2003},{"cited_arxiv_id":"","doi":"10.1016/j.dam.2025.12.025","is_internal_anchor":false,"ref_index":4,"title":"Discrete Applied Mathematics383, 85–93 (2026)","work_id":"ed16aaec-6e9d-4626-9bb4-b6d44b7f2641","year":2026},{"cited_arxiv_id":"","doi":"10.46298/dmtcs.2136","is_internal_anchor":false,"ref_index":5,"title":"Discrete Mathematics & Theoretical Computer Science17(2), 77–100 (2015)","work_id":"e05ab08c-e76c-427e-ae89-5c01ae5c0f81","year":2015}],"snapshot_sha256":"dcfdefb5c8c12d3a4cec0e3c097d6a1982e061f4b617d34d9376f60035239f2d"},"source":{"id":"2605.13299","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T19:02:45.963381Z","id":"11e280b8-7e99-4e73-9bc7-47d1c235229b","model_set":{"reader":"grok-4.3"},"one_line_summary":"Kernelization establishes FPT for strong CFVC number by twin cover plus k, with svcfc(G) bounded between χ(G) and χ(G) plus twin cover size.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A graph with twin cover of size t has strong conflict-free vertex-connection number at most its chromatic number plus t.","strongest_claim":"Given (G,k) together with a twin cover X of size t, we reduce in polynomial time to an equivalent annotated instance on at most max{2,t+(t+1)k 2^{t+k-1}} vertices. Every connected graph G with twin cover X of size t satisfies χ(G) ≤ svcfc(G) ≤ χ(G) + t.","weakest_assumption":"The kernelization result assumes a twin cover X is supplied as part of the input; the FPT claim for tc(G) + k therefore depends on either the cover being given or on the complexity of computing it separately."}},"verdict_id":"11e280b8-7e99-4e73-9bc7-47d1c235229b"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:57305ab3395d88996dc32dcda9c146e8f9c8568ea672e6f078bf1d9658f5c72d","target":"record","created_at":"2026-05-18T02:44:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cf35c419ebe748131ac7a76d0f046512d08b4b1f6d53d83c04ba7ac6a5ac939a","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2026-05-13T10:13:01Z","title_canon_sha256":"e401756958e668504b3b09e20c563c1d223ae8a52eb306e247e1a512b7c22894"},"schema_version":"1.0","source":{"id":"2605.13299","kind":"arxiv","version":1}},"canonical_sha256":"8d11efc51625d49bd9e53ccfb1f6da56358fb8e061b32caaaf0573a6b0622b10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d11efc51625d49bd9e53ccfb1f6da56358fb8e061b32caaaf0573a6b0622b10","first_computed_at":"2026-05-18T02:44:49.058184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:49.058184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1KCm7+Wzbs1Us9GWyXEJNmMJj6ZgRu4G7qPWotH8fFoeyPDmTBX21ng8yzhlx+/PhxPPQiF260MiECAMjDPABA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:49.058583Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13299","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57305ab3395d88996dc32dcda9c146e8f9c8568ea672e6f078bf1d9658f5c72d","sha256:ce0dfbbee91807f630416d7f3cd1a69f66a6a398e2b35afbacdba77c337c2053"],"state_sha256":"335fa0fc4c980f7ac53e259aecd7aed7fb092b7e5685806785870424ca02f10f"}