{"paper":{"title":"Computational methods for finding bi-regular cages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jan Goedgebeur, Jorik Jooken, Tibo Van den Eede","submitted_at":"2024-11-26T11:53:11Z","abstract_excerpt":"An $(\\{r,m\\};g)$-graph is a (simple, undirected) graph of girth $g\\geq3$ with vertices of degrees $r$ and $m$ where $2 \\leq r < m$ . Given $r,m,g$, we seek the $(\\{r,m\\};g)$-graphs of minimum order, called $(\\{r,m\\};g)$-cages or bi-regular cages, whose order is denoted by $n(\\{r,m\\};g)$. In this paper, we use computational methods for finding $(\\{r,m\\};g)$-graphs of small order. Firstly, we present an exhaustive generation algorithm, which leads to $\\unicode{x2013}$ previously unknown $\\unicode{x2013}$ exhaustive lists of $(\\{r,m\\};g)$-cages for 24 different triples $(r,m,g)$. This also leads "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17351","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/2411.17351/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"}