Year: 2017
Type: article
Abstract: We investigate the smallest number λ(G) of vertices that need to be removed from a non-empty graph G so that the resulting graph has a smaller maximum degree. We prove that if n is the number of vertices, k is the maximum degree, and t is the number of vertices of degree k, then λ(G) ≤ n+(k−1)t /2k . We also show that λ(G) ≤ n k+1 if G is a tree. These bounds are sharp. We provide other bounds together with structural observations.
Source: OAR@UM (University of Malta)
Authors: Borg, Peter, Fenech, Kurt
Institution: University of Malta
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7070813522