On minimal prime graphs and posets
Maurice Pouzet, Imed Zaguia
TL;DR
This paper classifies infinite prime graphs and posets by showing that they embed one of four specific prime graphs or posets, revealing structural patterns in infinite prime structures.
Contribution
It identifies four fundamental infinite prime graphs and extends the classification to infinite prime posets without infinite chains or antichains.
Findings
Four infinite prime graphs serve as universal embeddings for all such structures.
Similar classification applies to infinite prime posets without infinite chains or antichains.
Provides a structural understanding of prime graphs and posets in infinite cases.
Abstract
We show that there are four infinite prime graphs such that every infinite prime graph with no infinite clique embeds one of these graphs. We derive a similar result for infinite prime posets with no infinite chain or no infinite antichain.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph Labeling and Dimension Problems · Advanced Graph Theory Research