{"paper":{"title":"Towards a constructive formalization of Perfect Graph Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.LO","authors_text":"Abhishek Kr Singh, Raja Natarajan","submitted_at":"2018-12-28T16:46:37Z","abstract_excerpt":"Interaction between clique number $\\omega(G) $ and chromatic number $\\chi(G) $ of a graph is a well studied topic in graph theory. Perfect Graph Theorems are probably the most important results in this direction. Graph $G$ is called \\emph{perfect} if $\\chi(H)=\\omega(H)$ for every induced subgraph $H$ of $G$. The Strong Perfect Graph Theorem (SPGT) states that a graph is perfect if and only if it does not contain an odd hole (or an odd anti-hole) as its induced subgraph. The Weak Perfect Graph Theorem (WPGT) states that a graph is perfect if and only if its complement is perfect. In this paper,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11108","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}