Is there accepted name for digraph segement without "joins" or "turns"? As example lets consider following directed graph:
Z--                -->D
    \            / 
      ->A-->B-->C
    /            \
Y--                -->F

In A->B->C part there are no "joins"/"turns".
(opposite of that would be any path that includes A or C not as starting/ending vertex, as A has two incoming edges and C has two outgoing edges)
How one would unambiguously call that? (linear segment?)

Edit:
My attempt at clarification of the question.
Given graph $G$, is there accepted term for connected induced subgraph $H$,

which edges satisfy $\forall xy \in E(H) \Rightarrow (deg^+(x)_G\leq 1 \land deg^-(y)_G \leq 1) $?
(Subscript $G$ in $deg^+(x)_G$ marks that degree is counted in graph $G$ (as opposed to subgraph $H$))

Edit-2:
Couple of related terms/concepts:


*

*Subdivision and smoothing (also "Homeomorphism" under same link)

*Series-ReducedTree
 A: As I understand it, you're asking:

Question. What do we call--and how should we define--subgraphs with the following property?
  
  
*
  
*(Thinness) Given nodes $x$ and $y$, there is at most one path from $x$ to $y$.
  
*(Totality) Given nodes $x$ and $y$, either there is a path from $x$ to $y$, or there is a path from $y$ to $x$, or both.
  

Firstly, observe that the conditions for linearity are completely internal conditions--that is, they make no mention of the larger graph in which our subgraph is embedded. Hence, we can phrase the definition for digraphs themselves, rather than for subgraphs of digraphs.
With that out of the way, I would advise simply calling them linear:

Definition 0. A digraph $D$ is linear iff the category of paths of $D$ is both thin and total.

To complete the definition, we need to explain the terms "thin" and "total."

Definition 1. Let $\mathbf{C}$ denote a category. Then:
  
  
*
  
*$\mathbf{C}$ is thin iff every pair of parallel arrows is equal.
  
*$\mathbf{C}$ is total iff for all objects $X$ and $Y$, either there exists an arrow $X \rightarrow Y$, or there exists an arrow $Y \rightarrow X$, or both.
  

In summary, you can then say: "observe that the subgraph $\{A \rightarrow B \rightarrow C\}$ is linear" or "observe that the subgraph induced by $\{A,B,C\}$ is linear."
Lets now define:

Definition 2. Let $D$ denote a digraph. A turn in $D$ is a node $x$ of $D$ with out-degree $\geq 1$. That is, it is a node $x$ of $D$
   such that there exist distinct nodes $a,b$ of $D$ and arrows $x
 \rightarrow a$ and $x \rightarrow b$. A join in $D$ is a node $y$ of
   $d$ with in-degree $\geq 1$. That is, it is a node $x$ of $D$ such
   that there exist distinct nodes $a,b$ of $D$ and arrows $a
 \rightarrow x$ and $b \rightarrow x$.

You should then be able to prove:

Proposition. A digraph is linear iff it is connected, and has no joins or turns.

Note that the following digraph has no joins or turns, but nonetheless isn't linear according to our definition, because it isn't connected:
$$\left\{\begin{matrix}A_0 \rightarrow B_0 \rightarrow C_0\\A_1 \rightarrow B_1 \rightarrow C_1\end{matrix}\right\}$$
