Chain method for panchromatic colorings of hypergraphs
Margarita Akhmejanova, J\'ozsef Balogh

TL;DR
This paper establishes conditions under which hypergraphs can be colored with r colors so that every edge contains all colors, extending understanding of panchromatic colorings in hypergraph theory.
Contribution
It introduces a new chain method to prove the existence of panchromatic colorings for certain hypergraphs with bounded edge counts.
Findings
Proves existence of panchromatic colorings for hypergraphs with specific edge bounds.
Provides bounds on the number of edges for guaranteed panchromatic coloring.
Extends previous results to larger ranges of r and hypergraph sizes.
Abstract
We deal with an extremal problem concerning panchromatic colorings of hypergraphs. A vertex -coloring of a hypergraph is \emph{panchromatic} if every edge meets every color. We prove that for every , every -uniform hypergraph with has a panchromatic coloring with colors.
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Taxonomy
TopicsLimits and Structures in Graph Theory
