{"paper":{"title":"Excluding a Ladder as an Induced Minor in Graphs Without Induced Stars","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Mujin Choi, Sebastian Wiederrecht","submitted_at":"2025-09-04T09:00:07Z","abstract_excerpt":"A $k$-ladder is the graph obtained from two disjoint paths, each with $k$ vertices, by joining the $i$th vertices of both paths with an edge for each $i\\in\\{ 1,\\ldots,k\\}$. In this paper, we show that for all positive integers $k$ and $d$, the class of all $K_{1,d}$-free graphs excluding the $k$-ladder as an induced minor has a bounded tree-independence number.\n  We further show that our method implies a number of known results: We improve the bound on the tree-independence number for the class of $K_{1,d}$-free graphs not containing a wheel as an induced minor given by Choi, Hilaire, Milani\\v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.04026","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/2509.04026/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"}