2008/02/15 by Shai Gutner, Gutner, Shai
Computer Science · Mathematics · #Advanced Graph Theory Research #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #cs.CC #cs.DM #cs.DS
paper · pdf · doi:10.48550/arxiv.0802.2157
arxiv created 2008/02/15 · openalex publication_date 2008/02/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A solution to a problem of Erdős, Rubin and Taylor is obtained by showing that if a graph G is (a:b)-choosable, and c/d > a/b, then G is not necessarily (c:d)-choosable. The simplest case of another problem, stated by the same authors, is settled, proving that every 2-choosable graph is also (4:2)-choosable. Applying probabilistic methods, an upper bound for the kth choice number of a graph is given. We also prove that a directed graph with maximum outdegree d and no odd directed cycle is (k(d+1):k)-choosable for every k ≥ 1. Other results presented in this article are related to the strong choice number of graphs (a generalization of the strong chromatic number). We conclude with complexity analysis of some decision problems related to graph choosability.