A simple graph is
-indifferent if it admits a total
order

on its nodes such that every chordless path with nodes

and edges

has

or

.

-indifferent graphs
generalize indifferent graphs and are perfectly orderable. Recently, Hoàng,
Maffray and Noy gave a characterization of

-indifferent graphs in terms
of forbidden induced subgraphs. We clarify their proof and describe a linear
time algorithm to recognize

-indifferent graphs. When the input is a

-indifferent graph, then the algorithm computes an order

as
above