Single conflict coloring and palette sparsification of uniform hypergraphs
Carl Johan Casselgren, Kalle Eriksson

TL;DR
This paper introduces single conflict coloring for r-uniform hypergraphs, analyzes probabilistic models, and establishes thresholds and conditions for colorability, contributing new theoretical insights into hypergraph coloring.
Contribution
It presents the concept of single conflict coloring, studies probabilistic thresholds, and provides palette sparsification results for linear uniform hypergraphs.
Findings
Sharp threshold for complete graphs in the probabilistic model
Sufficient condition for single conflict colorability in hypergraphs
Palette sparsification results for linear uniform hypergraphs
Abstract
We introduce and investigate single conflict coloring in the setting of r-uniform hypergraphs. We establish some basic properties of this hypergraph coloring model and study a probabilistic model of single conflict coloring where the conflicts for each edge are chosen randomly; in particular, we prove a sharp threshold-type result for complete graphs and establish a sufficient condition for single conflict colorability of r-uniform hypergraphs in this model. Furthermore, we obtain a related palette sparsification-type result for general list coloring of linear uniform hypergraphs (i.e. uniform hypergraphs where any two edges share at most one common vertex). Throughout the paper we pose several questions and conjectures
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Complexity and Algorithms in Graphs
