Graph Theory: Lecture No. 8
A path cover of a directed graph Gis a set of
disjoint paths in Gwhich together contain all
the vertices of G.
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Graph Theory: Lecture No. 8 - Path Covers and Comparability Graphs, Slides of Design and Analysis of Algorithms
This document from graph theory: lecture no. 8 discusses path covers in directed graphs, their relationship with independent sets, the minimum number of chains in partially ordered sets, and the concept of comparability graphs. It also explains how edges in comparability graphs can be transitively oriented.
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2012/2013
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A path cover of a directed graph G is a set of disjoint paths in G which together contain all the vertices of G.
Every directed graph G has a path cover P and independent set {vP : P ∈ P} of vertices such that vP ∈ P for every P ∈ P.
A graph G = (V , E ) is a comparability graph if and only if its edges can be transitively oriented.