Abstract
Many graphs which are encountered in the study of graph theory are characterized by a type of configuration or subgraph they possess. However, there are occasions when such graphs are more easily defined or described by the kind of subgraphs they are not permitted to contain. For example, a tree can be defined as a connected graph which contains no cycles, and Kuratowski [22] characterized planar graphs as those graphs which fail to contain subgraphs homeomorphic from the complete graph K 5 or the complete bipartite graph K 3,3. The purpose of this article is to study, in a unified manner, several classes of graphs, which can be defined in terms of the kinds of subgraphs they do not contain, and to investigate related concepts. In the process of doing this, we show that many “apparently unrelated” results in the literature of graph theory are closely related. Several unsolved problems and conjectures are also presented.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
