SelfContained Graphs
Abstract
A selfcontained 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 substructures 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2015
 arXiv:
 arXiv:1503.00139
 Bibcode:
 2015arXiv150300139H
 Keywords:

 Mathematics  Combinatorics;
 05C63;
 05C60