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A proper edge $t$-coloring of a graph $G$ is a coloring of edges of $G$ withcolors $1,2,...,t$ such that each of $t$ colors is used, and adjacent edges arecolored differently. The set of colors of edges incident with a vertex $x$ of$G$ is called a spectrum of $x$. A proper edge $t$-coloring of a graph $G$ isinterval for its vertex $x$ if the spectrum of $x$ is an interval of integers.A proper edge $t$-coloring of a graph $G$ is persistent-interval for its vertex$x$ if the spectrum of $x$ is an interval of integers beginning from the color1.  For graphs $G$ from some classes of graphs, we obtain estimates for thepossible number of vertices for which a proper edge $t$-coloring of $G$ can beinterval or persistent-interval.

Estimates for the number of vertices with an interval spectrum in proper edge colorings of some graphs