A graph with the partial order competition dimension greater than five
Jihoon Choi, Soogang Eoh, and Suh-Ryung Kim
TL;DR
This paper demonstrates the existence of a graph with a partial order competition dimension exceeding five, using combinatorial methods to advance understanding of graph dimensions.
Contribution
It introduces a new result showing that some graphs have a partial order competition dimension greater than five, expanding the known bounds.
Findings
Existence of graphs with partial order competition dimension > 5
Application of Erdős-Szekeres lemma in graph theory
Advancement in understanding graph dimension bounds
Abstract
In this paper, we use the Erd\"{o}s-Szekeres lemma to show that there exists a graph with partial order competition dimension greater than five.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Graph theory and applications