# Longest Path on Interval Graphs (Longest Path Problem)

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## Description

The longest path problem is the problem of finding a path of maximum length in a graph.

A graph $G$ is called interval graph if its vertices can be put in a one-to-one correspondence with a family $F$ of intervals on the real line such that two vertices are adjacent in $G$ if and only if the corresponding intervals intersect; $F$ is called an intersection model for $G$.

## Parameters

$n$: number of vertices

$m$: number of edges

## Table of Algorithms

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

Ioannidou; Kyriaki; Mertzios; George B.; Nikolopoulos; Stavros D. | 2011 | $O(n^{4})$ | $O(n^{3})$ | Exact | Deterministic | Time & Space |