2011/08/24 by Jacob Fox, Fox, Jacob
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1108.4953
openalex publication_date 2011/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mader asked to explicitly construct dense graphs for which the size of the largest clique minor is sublinear in the number of vertices. Such graphs exist as a random graph almost surely has this property. This question and variants were popularized by Thomason over several articles. We answer these questions by showing how to explicitly construct such graphs using blow-ups of small graphs with this property. This leads to the study of a fractional variant of the clique minor number, which may be of independent interest.