Home > Journals > TAG > Vol. 5 > Iss. 2 (2018)
Abstract
Let λ(G) denote the smallest number of vertices that can be removed from a non-empty graph G so that the resulting graph has a smaller maximum degree. In a recent paper, we proved that if n is the number of vertices of G,k is the maximum degree of G, and t is the number of vertices of degree k, then λ: (G) ≤ n+(k-1)t}{2k}. We also showed that λ (G) ≤ \frac{n}{k+1} if G is a tree. In this paper, we provide a new proof of the first bound and use it to determine the graphs that attain the bound, and we also determine the trees that attain the second bound.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Borg, Peter and Fenech, Kurt
(2018)
"Reducing the maximum degree of a graph by deleting vertices: the extremal cases,"
Theory and Applications of Graphs: Vol. 5:
Iss.
2, Article 5.
DOI: 10.20429/tag.2018.050205
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol5/iss2/5
Supplemental file with DOI