A New Definition of the Dimension of Graphs
X.Zhao
TL;DR
This paper introduces a novel way to define the dimension of graphs, inspired by recent work on the sensitivity conjecture, and explores its connection to the chromatic number.
Contribution
It proposes a new graph dimension definition and establishes a relationship between this dimension and the chromatic number.
Findings
New graph dimension definition proposed
Relationship established between dimension and chromatic number
Inspired by recent sensitivity conjecture work
Abstract
Enlighted by the recent work of Hao Huang on sensitivity conjecture [arXiv:1907.00847], we propose a new definition of the dimension of graphs and establish a relationship between the chromatic number and the dimension.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research