Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
157 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

List Coloring Triangle-Free Hypergraphs (1302.3872v1)

Published 15 Feb 2013 in math.CO

Abstract: A triangle in a hypergraph is a collection of distinct vertices u,v,w and distinct edges e,f,g with u,v \in e, v,w \in f, w,u \in g, and {u,v,w} \cap e \cap f \cap g=\emptyset. The i-degree of a vertex in a hypergraph is the number of edges of size i containing it. We prove that every triangle-free hypergraph of rank three (edges have size two or three) with maximum 3-degree \Delta_3 and maximum 2-degree \Delta_2 has list chromatic number at most c max{\Delta_2/ log{\Delta_2}}, (\Delta_3 / log{\Delta_3})1/2} for some absolute positive constant c. This generalizes a result of Johansson and a result of Frieze and the second author.

Summary

We haven't generated a summary for this paper yet.