{"ID":2851294,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.20744","arxiv_id":"2510.20744","title":"A Freeable Matrix Characterization of Bipartite Graphs of Ferrers Dimension Three","abstract":"Ferrer dimension, along with the order dimension, is a standard dimensional concept for bipartite graphs. In this paper, we prove that a graph is of Ferrer dimension three (equivalent to the intersection bigraph of orthants and points in ${\\mathbb R}^3$) if and only if it admits a biadjacency matrix representation that does not contain $Γ= \\begin{bmatrix} * \u0026 1 \u0026 * \\\\ 1 \u0026 0 \u0026 1 \\\\ 0 \u0026 1 \u0026 * \\end{bmatrix}$ and $Δ= \\begin{bmatrix} 1 \u0026 * \u0026 * \\\\ 0 \u0026 1 \u0026 * \\\\ 1 \u0026 0 \u0026 1 \\end{bmatrix}$, where $*$ denotes zero or one entry.","short_abstract":"Ferrer dimension, along with the order dimension, is a standard dimensional concept for bipartite graphs. In this paper, we prove that a graph is of Ferrer dimension three (equivalent to the intersection bigraph of orthants and points in ${\\mathbb R}^3$) if and only if it admits a biadjacency matrix representation that...","url_abs":"https://arxiv.org/abs/2510.20744","url_pdf":"https://arxiv.org/pdf/2510.20744v1","authors":"[\"Parinya Chalermsook\",\"Ly Orgo\",\"Minoo Zarsav\"]","published":"2025-10-23T17:09:06Z","proceeding":"math.CO","tasks":"[\"math.CO\",\"cs.DS\"]","methods":"[]","has_code":false}