Self-Contained Graphs
Combinatorics
2016-11-04 v2
Abstract
A self-contained graph is an infinite graph which is isomorphic to one of its proper induced subgraphs. In this paper, these graphs are studied by presenting some examples and defining some of their sub-structures such as removable subgraphs and the foundation. Then, we show that the general version of graph alternative conjecture, which says every graph has infinitely many strong twins or none, can be deduced from its connected version, which says every connected graph has infinitely many connected strong twins or none. Moreover, we try to find out under what conditions on two arbitrary removable subgraphs, their union is also a removable subgraph.
Cite
@article{arxiv.1503.00139,
title = {Self-Contained Graphs},
author = {Mohammad Hadi Shekarriz and Madjid Mirzavaziri},
journal= {arXiv preprint arXiv:1503.00139},
year = {2016}
}