# All Maximal Non-Branching Paths in a Graph (All Maximal Non-Branching Paths in a Graph)

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## Description

A node $v$ in a directed graph $G$ is called a 1-in-1-out node if its indegree and outdegree are both equal to 1, i.e., $in(v) = out(v) = 1$. We can rephrase the definition of a "maximal non-branching path" from the main text as a path whose internal nodes are 1-in-1-out nodes and whose initial and final nodes are not 1-in-1-out nodes.

The problem is to find all maximal non-branching paths in a given graph.

## Parameters

$n$: number of vertices

$m$: number of edges

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Naive | 1940 | $O(m)$ | $O(n)$? | Exact | Deterministic | Time |