[INFO] star-width

[michalddvorak]

vertex integrity is also sometimes known as star-width, i.e. I want a tree decomposition of the graph where the tree is a star.

definition: https://www.sciencedirect.com/science/article/pii/S0020019017300704
but no relation to vi there...,
the proof of equivalence is roughly as follows:
sw -> vi
the root of the decomposition is the separator to the vertex integrity
vi -> sw
the separator forms the root of the decomposition, everything else is maybe connected to it -> star-decomoposition

[vaclavblazej]

Thanks, I'll add this with the next update which may take some time now due to holidays. From what you say it seems to be functionally equivalent but not equal to vi. Let me know if you stumble upon other publications on star-width.