Document Type
Article
Publication Date
3-6-2019
Publication Title
arXiv: Combinatorics
Keywords
Combinatorics
Disciplines
Discrete Mathematics and Combinatorics | Mathematics
Abstract
In this paper we prove that the recursive (Knill) dimension of the join of two graphs has a simple formula in terms of the dimensions of the component graphs: dim(G1+G2)=1+dimG1+dimG2. We use this formula to derive an expression for the Knill dimension of a graph from its minimum clique cover. A corollary of the formula is that a graph made of the arbitrary union of complete graphs KN of the same order N will have dimension N−1. We finish by finding lower and upper bounds on the Knill dimension of a graph in terms of its clique number.
Recommended Citation
Kassahun Betre and Evatt Salinger. "The Knill Graph Dimension from The Minimum Clique Cover" arXiv: Combinatorics (2019).
Comments
Published on arXiv.org: https://arxiv.org/abs/1903.02523 This paper has now been published under the title "The Inductive Graph Dimension from the Minimum Edge Clique Cover" in the journal Graphs and Combinatorics in Novebmer 2021. It can be read here: https://doi.org/10.1007/s00373-021-02381-y