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Once every vertex is coloured, Alice wins if there is a connected red component of order at least $k$, and otherwise, Bob wins. This is a Maker-Breaker version of the Largest Connected Subgraph game introduced in [Bensmail et al. The Largest Connected Subgraph Game. {\\it Algorithmica}, 84(9):2533--2555, 2022]. We want to compute $c_g(G)$, which is the maximum $k$ such that Alice wins in $G$, regardless"},"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":"2402.12811","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2024-02-20T08:28:59Z","cross_cats_sorted":[],"title_canon_sha256":"a33400529bc5440328f7a41a3e1dc179859ae4edf31f2468981e41a6876906a2","abstract_canon_sha256":"ebf10212138a0005eb216c494d7f8be91c8f6ce18706fa176463d1676fd0ad3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:47:16.829815Z","signature_b64":"YlSksvuGI2gPsHOiRRCTqoPdSOT2lrP+cvD0sX7Yhah6trfnjZ5YpAKMUMM2t0trdyKrcEiihs+jx9yJoxxDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a78bc853b7a986eaaad33d313eef3438b36af3c0d82865942a333ed8f4991a08","last_reissued_at":"2026-07-05T07:47:16.829417Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:47:16.829417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Maker-Breaker Largest Connected Subgraph Game","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fionn Mc Inerney, Foivos Fioravantes, Julien Bensmail, Nacim Oijid, Nicolas Nisse","submitted_at":"2024-02-20T08:28:59Z","abstract_excerpt":"Given a graph $G$ and $k \\in \\mathbb{N}$, we introduce the following game played in $G$. 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