{"paper":{"title":"On Supports for graphs of bounded genus","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Karamjeet Singh, Rajiv Raman","submitted_at":"2025-03-27T09:11:24Z","abstract_excerpt":"Let $(X,\\mathcal{E})$ be a hypergraph. A support is a graph $Q$ on $X$ such that for each $E\\in\\mathcal{E}$, the subgraph of $Q$ induced on the elements in $E$ is connected. We consider the problem of constructing a support for hypergraphs defined by connected subgraphs of a host graph. For a graph $G=(V,E)$, let $\\mathcal{H}$ be a set of connected subgraphs of $G$. Let the vertices of $G$ be partitioned into two sets the \\emph{terminals} $\\mathbf{b}(V)$ and the \\emph{non-terminals} $\\mathbf{r}(V)$. We define a hypergraph on $\\mathbf{b}(V)$, where each $H\\in\\mathcal{H}$ defines a hyperedge con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.21287","kind":"arxiv","version":6},"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/2503.21287/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"}