Loading...

On the chromatic vertex stability number of graphs

Akbari, S ; Sharif University of Technology | 2022

6 Viewed
  1. Type of Document: Article
  2. DOI: 10.1016/j.ejc.2021.103504
  3. Publisher: Academic Press , 2022
  4. Abstract:
  5. The chromatic vertex (resp. edge) stability number vsχ(G) (resp. esχ(G)) of a graph G is the minimum number of vertices (resp. edges) whose deletion results in a graph H with χ(H)=χ(G)−1. In the main result it is proved that if G is a graph with χ(G)∈{Δ(G),Δ(G)+1}, then vsχ(G)=ivsχ(G), where ivsχ(G) is the independent chromatic vertex stability number. The result need not hold for graphs G with [Formula Presented]. It is proved that if [Formula Presented], then vsχ(G)=esχ(G). A Nordhaus–Gaddum-type result on the chromatic vertex stability number is also given. © 2021 Elsevier Ltd
  6. Keywords:
  8. Source: European Journal of Combinatorics ; Volume 102 , 2022 ; 01956698 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0195669821001980