Graphs that are minor minimal with respect to dimension

Autor:	Giardina, Thomas, Foisy, Joel
Rok vydání:	2021
Předmět:	Mathematics - Combinatorics 05C10 (Primary) 05C83 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Erd\H{o}s, Harary, and Tutte defined the dimension of a graph $G$ as the smallest natural number $n$ such that $G$ can be embedded in $\mathbb{R}^n$ with each edge a straight line segment of length 1. Since the proposal of this definition, little has been published on how to compute the exact dimension of graphs and almost nothing has been published on graphs that are minor minimal with respect to dimension. This paper develops both of these areas. In particular, it (1) establishes certain conditions under which computing the dimension of graph sums is easy and (2) constructs three infinitely-large classes of graphs that are minor minimal with respect to their dimension. Comment: 26 pages, 9 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2106.05930 Zobrazit plný text záznamu View this record from Arxiv