Induced Subgraph Saturated Graphs

Authors

Craig M. Tennenhouse, University of New EnglandFollow

Publication Date

2016

Abstract

A graph G is said to be H-saturated if G contains no subgraph isomorphic to H but the addition of any edge between non-adjacent vertices in G creates one. While induced subgraphs are often studied in the extremal case with regard to the removal of edges, we extend saturation to induced subgraphs. We say that G is induced H-saturated if G contains no induced subgraph isomorphic to H and the addition of any edge to G results in an induced copy of H. We demonstrate constructively that there are non-trivial examples of saturated graphs for all cycles and an infinite family of paths and find a lower bound on the size of some induced path-saturated graphs.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Tennenhouse, Craig M. (2016) "Induced Subgraph Saturated Graphs," Theory and Applications of Graphs: Vol. 3: Iss. 2, Article 1.
DOI: 10.20429/tag.2017.030201
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol3/iss2/1