2007/01/18 by David Romero, Abdón S ́nchez-Arroyo · 1 citation
Computer Science · Engineering · Mathematics · #Graph Labeling and Dimension Problems #Advanced Graph Theory Research #graph theory and CDMA systems #Conjecture #Combinatorics #Hypergraph #Vertex (graph theory) #Mathematics #Generality #Discrete mathematics #Graph
paper · doi:10.1093/acprof:oso/9780198571278.003.0017
openalex publication_date 2007/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
A hypergraph is linear if no two distinct edges intersect in more than one vertex. A well-known conjecture of Erdős, Faber, and Lovász states that if a linear hypergraph has n edges, each of size n, then there is a n-vertex colouring of the hypergraph such that each edge contains one vertex of each colour. Dating back to 1972, it is very surprising that this conjecture has not been settled in its full generality. This chapter presents some advances on it.