{"paper":{"title":"Minkowski decomposability of symmetric edge polytopes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Aki Mori","submitted_at":"2026-08-03T16:23:46Z","abstract_excerpt":"In this paper, we study the Minkowski decomposability of symmetric edge polytopes $P_G^\\pm$ of a finite simple graph $G$ on vertex set $[n]$. More precisely, we give a complete characterization of graphs whose symmetric edge polytopes are Minkowski decomposable. We prove that $P_G^\\pm$ is Minkowski decomposable if and only if $G$ is one of the three complete multipartite graphs: $K_n$, $K_{2,n-2}$, or $K_{1,1,n-2}$. In other words, if $G$ does not belong to these three families, then $P_G^\\pm$ is Minkowski indecomposable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02445","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.02445/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}