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For a 2-coloring $f$, let $r'_f$ and $b'_f$ be the number of red and blue edges and let $\\mu_f(G)=\\min\\{r'_f,b'_f\\}$. Let $\\mu(G)$ be the maximum of $\\mu_f(G)$ over all 2-colorings.\n  We introduce the parameterized problem $k$-LCP of deciding whether $\\mu(G)\\ge k$, where $k$ is the parameter. We prove that this problem admits a kernel with at most $7k$. Ahuja e"},"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":"1308.1820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-08T11:41:30Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"96b85811c704d5f68551bc3ca8ecba718683b82978b242d0443512f8c53609a3","abstract_canon_sha256":"d4c74d6c2a1440e12e799ce3883e45ff23aaa1abe98cf197b89ba2d74a0b19a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:18.378757Z","signature_b64":"iPW8bFXJEVoLgOlbzXgqcW14Lhrj+sNjIdppenAuXot2GnoyP98/6rnP8Vi/eqjWFO09RVuyJ3cP1DTzuJ9yDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf6ccfa83db5c6198841db5e4ccc2dbdf1622087da0d24e159dd9abfded031ca","last_reissued_at":"2026-05-18T02:55:18.378371Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:18.378371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parameterized Algorithms for Load Coloring Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Gregory Gutin, Mark Jones","submitted_at":"2013-08-08T11:41:30Z","abstract_excerpt":"One way to state the Load Coloring Problem (LCP) is as follows. Let $G=(V,E)$ be graph and let $f:V\\rightarrow \\{{\\rm red}, {\\rm blue}\\}$ be a 2-coloring. An edge $e\\in E$ is called red (blue) if both end-vertices of $e$ are red (blue). For a 2-coloring $f$, let $r'_f$ and $b'_f$ be the number of red and blue edges and let $\\mu_f(G)=\\min\\{r'_f,b'_f\\}$. Let $\\mu(G)$ be the maximum of $\\mu_f(G)$ over all 2-colorings.\n  We introduce the parameterized problem $k$-LCP of deciding whether $\\mu(G)\\ge k$, where $k$ is the parameter. We prove that this problem admits a kernel with at most $7k$. 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