k --Universal Finite Graphs
Logic
2016-09-06 v1
Abstract
This paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics. The main results of the paper, which are due to Shelah, establish that the class of k-universal graphs is not definable by an infinite disjunction of first-order existential sentences with a finite number of variables and that there exist k-universal graphs with no k-extendible induced subgraphs.
Keywords
Cite
@article{arxiv.math/9604244,
title = {k --Universal Finite Graphs},
author = {Eric Rosen and Saharon Shelah and Scott Weinstein},
journal= {arXiv preprint arXiv:math/9604244},
year = {2016}
}