Application of an Extremal Result of Erdős and Gallai to the (n,k,t) Problem

Authors

Matt Noble, Middle Georgia State UniversityFollow
Peter Johnson, Auburn University Main CampusFollow
Dean Hoffman, Auburn UniversityFollow
Jessica McDonald, Auburn UniversityFollow

Publication Date

2017

Abstract

An extremal result about vertex covers, attributed by Hajnal to Erdős and Gallai, is applied to prove the following: If n, k, and t are integers satisfying n ≥ k ≥ t ≥ 3 and k ≤ 2t - 2, and G is a graph with the minimum number of edges among graphs on n vertices with the property that every induced subgraph on k vertices contains a complete subgraph on t vertices, then every component of G is complete.

Creative Commons License

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

Recommended Citation

Noble, Matt; Johnson, Peter; Hoffman, Dean; and McDonald, Jessica (2017) "Application of an Extremal Result of Erdős and Gallai to the (n,k,t) Problem," Theory and Applications of Graphs: Vol. 4: Iss. 2, Article 1.
DOI: 10.20429/tag.2017.040201
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol4/iss2/1