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A graph $G$ is b-continuous if $G$ has a b-coloring with $k$ colors, for every integer $k$ in the interval $[\\chi(G),\\chi_b(G)]$. It is known that not all graphs are b-continuous. Here, we investigate whether the lexicographic product $G[H]$ of b-continuous graphs $G$ and $H$ is also b-continuous. Using homomorphisms, we provide a"},"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":"1610.03084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-10-10T20:28:41Z","cross_cats_sorted":[],"title_canon_sha256":"0bbd922deb776e96794689711d20c1c6c9edc175ce86b3198f17431acc01e7e2","abstract_canon_sha256":"21fd59ded89c4467eddd7a9227de7bec8c18e36bced8692a42dbc1d53217a5be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:49.644078Z","signature_b64":"U7CYuGcPu4AItfPFuh3SIndLf7FIovqkgXqoRQ1a/gptzynEY2zkWU+6qXvMRaqiMCl4mlbpFpqCNKAXc00FDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdd7cd68eef41f821a98bbff5e501ed0b6c2c110632b82dd65856e6209c164cf","last_reissued_at":"2026-05-18T01:02:49.643661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:49.643661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the b-continuity of the lexicographic product of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Ana Silva, Cl\\'audia Linhares Sales, Leonardo Sampaio","submitted_at":"2016-10-10T20:28:41Z","abstract_excerpt":"A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to each other color class. The b-chromatic number of $G$ is the maximum integer $\\chi_b(G)$ for which $G$ has a b-coloring with $\\chi_b(G)$ colors. A graph $G$ is b-continuous if $G$ has a b-coloring with $k$ colors, for every integer $k$ in the interval $[\\chi(G),\\chi_b(G)]$. It is known that not all graphs are b-continuous. Here, we investigate whether the lexicographic product $G[H]$ of b-continuous graphs $G$ and $H$ is also b-continuous. 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