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A proper coloring of edges of $G$ with the colors $1,\\ldots,t$ is called interval (respectively, continuous) on $R$, if each color is used for at least one edge and the edges incident with each vertex $x\\in R$ are colored by $d(x)$ consecutive colors (respectively, by the colors $1,\\ldots,d(x))$, where $d(x)$ is a degree of the vertex $x$. We denote by $w_1(G)$ and $W_1(G)$, respectively, the least and the greatest values of $t$, for which there exists an interval on $V_1(G)$ coloring of the multigraph "},"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":"1401.8079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-31T07:54:40Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f78525132efff9a07241979f759be931cabe4b90826a8658b97ff6228459cfe3","abstract_canon_sha256":"ea7c4426045f026bc2535aad0d4e725cfc4e350aa17747653c0782bd58c72b4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:36.213210Z","signature_b64":"sKT7qzmhVb1flw4RxbKTlwcaygKqt2ZYVhFbB+aOsLAc4OqGCorCuIluaVC5sSX6L4kQgryO6BYqcuBpGpYaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f40d1f8838ad5b27871275ff7ea435226bf2996a833aee66cda5eb07d6dbfe3","last_reissued_at":"2026-05-18T03:00:36.212389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:36.212389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interval colorings of edges of a multigraph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"A.S. 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