A simple graph is
-indifferent if it admits a total
order
![$<$](Abs/img2.gif)
on its nodes such that every chordless path with nodes
![$a,b,c,d$](Abs/img3.gif)
and edges
![$ab,bc,cd$](Abs/img4.gif)
has
![$a<b<c<d$](Abs/img5.gif)
or
![$a>b>c>d$](Abs/img6.gif)
.
![$P_4$](Abs/img1.gif)
-indifferent graphs
generalize indifferent graphs and are perfectly orderable. Recently, Hoàng,
Maffray and Noy gave a characterization of
![$P_4$](Abs/img1.gif)
-indifferent graphs in terms
of forbidden induced subgraphs. We clarify their proof and describe a linear
time algorithm to recognize
![$P_4$](Abs/img1.gif)
-indifferent graphs. When the input is a
![$P_4$](Abs/img1.gif)
-indifferent graph, then the algorithm computes an order
![$<$](Abs/img2.gif)
as
above