List all induced subgraphs which are paths of length 4.
My understanding of this question is to list all the combinations of paths (no repeated vertices) of length $4$. For example
$a, b, c, d, e$
$b,c,d,e,f$
$a,d,c,b,h$
and other combinations of paths of $5$ vertices.
Have I understood this correctly?
For a graph $G = (V, E)$ and for any $W \subset V$, the induced subgraph $G[W]$ contains all edges between vertices in $W$. Hence the graph induced on $a, b, c, d, e$ is not actually a path of length 4 since $c$ is also connected to $e$ which forms a loop in the induced subgraph.