On Chromatic Vertex Stability of 3-Chromatic Graphs With Maximum Degree 4

Abstract

The (independent) chromatic vertex stability (ivs χ ( G )) vs χ ( G ) is the minimum size of (independent) set S ⊆ V ( G ) such that χ ( G − S ) = χ ( G ) − 1. In this paper we construct infinitely many graphs G with ∆( G ) = 4, χ ( G ) = 3, ivs χ ( G ) = 3 and vs χ ( G ) = 2, which gives a partial negative answer to a problem posed in [3].