{"paper":{"title":"The minimum degree question for the Maker Breaker Domination Game","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Georg Grasegger, Jakob F\\\"uhrer, Oliver Roche-Newton, Paul Hametner","submitted_at":"2026-06-03T12:46:11Z","abstract_excerpt":"The Maker Breaker Domination Game is a two player game played on a graph $G$ in which the players take turns to claim a vertex from the graph. The aim of the Dominator is to claim the vertices of a dominating set, and the aim of the Staller is to prevent this. In this paper, we consider the following problem: for a given integer $d$, what is the size of the smallest (with respect to the number of vertices) graph with minimum degree $d$ such that the Dominator loses going first? We write $\\beta(d)$ to denote the answer to this question. We determine the precise value of $\\beta(d)$ for $d\\leq 3$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04824","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/2606.04824/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"}