On the chromatic vertex stability number of graphs

The chromatic vertex (resp. edge) stability number vs chi(G) (resp. es(chi)(G)) of a graph G is the minimum number of vertices (resp. edges) whose deletion results in a graph H with chi(H) = chi(G)-1. In the main result it is proved that if G is a graph with chi(G) & ISIN; { increment (G), increment (G) + 1}, then vs chi(G) =delta(G), where ivs chi(G) is the independent chromatic vertex stability number. The result need not hold for graphs G with chi(G) <= delta (G)+1 /2 & nbsp;. It is proved that if chi(G) > increment (G) 2 + 1, then vs chi(G) = es chi(G). A Nordhaus-Gaddum-type result on the chromatic vertex stability number is also given.(C) 2021 Elsevier Ltd. All rights reserved.