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For a given class of graphs ${\\cal F}$, let $c({\\cal F}):=\\sup\\{c(F)|F\\in {\\cal F}\\}$, and let Forb$({\\cal F})$ denote the class of ${\\cal F}$-free graphs. We show that the complement of the Shrikhande graph is $(4K_1,C_{\\ell}$)-free for any $\\ell \\geq 6$ and has the cop number~$3$. This provides a counterexample for the conjecture proposed by Sivaraman (arxiv, 2019)"},"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":"2505.15416","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DM","submitted_at":"2025-05-21T12:00:32Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"aeae45c229460014a79011e47dedbe50c96688a756012e979318c452779b2bf8","abstract_canon_sha256":"b9c58e3c4935709d6688ec75ca77b8d812a3ad8055767fcc8aaa03903494c702"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:45.226071Z","signature_b64":"W0zmx1GfLgXrlwQJ0F7HwX5vL6Xv87GnsvUbl66TGcAPjwQoDelt/QwbBQp/RT+wgyu94Np2c7cj1uKQc77dAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40c5b3bb9bee68b94ea5e0fda99bd58feb3be7cc20171ecd76e0a3ea363b5405","last_reissued_at":"2026-07-05T11:06:45.225598Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:45.225598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$4K_1$-free graph with the cop number $3$","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Arnab Char, Dinabandhu Pradhan, Paras Vinubhai Maniya","submitted_at":"2025-05-21T12:00:32Z","abstract_excerpt":"The game of cops and robber is a two-player turn-based game played on a graph where the cops try to capture the robber. 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