Consider a graph $G=(V, E)$ with $|V|=n$ vertices. Let $(v_1, \dots, v_n)$ be an ordered list of its vertices. Let $G_i=G[\{v_{i+1}, \dots, v_n\}]$ be the induced subgraph on the last $n-i$ vertices. Let $(d_1, \dots, d_n)$ be the degree sequence of $G_i$: $d_i$ is the degree of $v_i$ in $G_i$.

**I wonder whether such sequences have been studied**, as they raise natural and interesting questions.

For instance, my original motivation is to obtain, for a given graph, such a sequence that is maximum with respect to the majorization order. A natural strategy would be to choose $v_1$ with maximum degree in $G_0$, $v_2$ with maximum degree in $G_1$, and so on. But there is an ambiguity when several vertices have the maximum degree, and other sequences may make sense.

Thank you for any information and suggestions.

somewhatrelated questions were posted here: mathoverflow.net/questions/378933/random-subgraph-properties and here: mathoverflow.net/questions/381631/… $\endgroup$