Is a − path followed by a − path is a − path.

Question

Can I say a − path followed by a − path is a − path.

Because if there is a path from − followed by − I believe there should be a − path.

I don't know how to prove it.

EDIT: A − path is a path between vertex and vertex. and − path is a path between vertex and vertex

A walk is a sequence of vertices and edges of a graph i.e. if we traverse a graph, then we get a walk.

A path is a walk with no repeated vertex. This directly implies that no edges will ever be repeated

Answer 1

Imagine that the $vw$ path contains the vertex $u$, the concatenation of $uv$ and $vw$ is not a path, but a walk. To be a path, you have to make sure it does not contains two identical vertices.

Answer 2

Hint: If $f,g:[0,1]\to X$ and $f(1)=g(0)$, then $h:[0,1]\to X$ and $h(0)=f(0)$ and $h(1)=g(1)$, where $$h(t) = \begin{cases} f(2t),& 0\leq t <\tfrac12\\ g(2t-1),& \tfrac12 \leq t \leq 1 \end{cases}$$