Chromatic Numbers of Algebraic Hypergraphs
James H. Schmerl
TL;DR
This paper determines the chromatic numbers of all infinite algebraic hypergraphs, which are hypergraphs defined by polynomial zero sets in Euclidean space, advancing understanding of their coloring properties.
Contribution
It provides a complete characterization of the chromatic numbers for all infinite algebraic hypergraphs, a previously unresolved problem.
Findings
Chromatic numbers of all infinite algebraic hypergraphs are explicitly determined.
The results unify algebraic and combinatorial perspectives in hypergraph coloring.
The paper introduces methods to analyze polynomial-defined hypergraph structures.
Abstract
A k-uniform hypergraph is algebraic if its vertex set is n-dimensional Euclidean space, for some n, and its hyperedge set is defined from the zero set of some polynomial. The chromatic numbers of all algebraic hypergraphs are determined, provided they are infinite.
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Taxonomy
TopicsLimits and Structures in Graph Theory · graph theory and CDMA systems · Graph Labeling and Dimension Problems