2024/08/05 by Raphael Steiner, Steiner, Raphael
Business, Management and Accounting · Computer Science · #05C15 #05C69 #Combinatorics (math.CO) #FOS: Mathematics #Image Retrieval and Classification Techniques #Optics and Image Analysis
paper · pdf · doi:10.48550/arxiv.2408.02400
openalex publication_date 2024/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The cochromatic number ζ(G) of a graph G is the smallest number of colors in a vertex-coloring of G such that every color class forms an independent set or a clique. In three papers written around 1990, Erdős, Gimbel and collaborators raised several open problems regarding the relationship of the chromatic and cochromatic number of a graph. In this short note, we address several of these problems, in particular -we disprove a conjecture of Erdős, Gimbel and Straight from 1988, -answer negatively a problem posed by Erdős and Gimbel in 1993, and -give positive evidence for a 1000$--question of Erdős and Gimbel.