A New Definition of the Dimension of Graphs

2019/08/10 by Xinrui Zhao, Zhao, X.
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.1908.03797

openalex publication_date 2019/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On the metric dimension, the upper dimension and the resolving number of\n graphs
• Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results
• On the Boolean dimension of a graph and other related parameters
• Graphs that are minor minimal with respect to dimension
• Graph Hausdorff dimension, Kolmogorov complexity and construction of fractal graphs