Nordhaus-Gaddum and other bounds for the chromatic edge-stability number

Abstract Let G be a graph. The chromatic edge-stability number es χ ( G ) of a graph G is the minimum number of edges of G whose removal results in a graph H with χ ( H ) = χ ( G ) − 1 . A Nordhaus–Gaddum type inequality for the chromatic edge-stability number is proved. Sharp upper bounds on es χ are given for general graphs in terms of size and of maximum degree, respectively. All bounds are demonstrated to be sharp. Graphs with es χ = 1 are considered and in particular characterized among k -regular graphs for k ≤ 5 . Several open problems are also stated.

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