1: Prove the directed version of Veblen's Theorem : A directed graph admits a decomposition into directed cycles if and only if its even. 2: Show that a graph G is connected if and only if there is an (X,Y) - path in G for any two nonempty subsets X and Y of V.
1: Prove the directed version of Veblen's Theorem : A directed graph admits a decomposition into directed cycles if and only if its even. 2: Show that a graph G is connected if and only if there is an (X,Y) - path in G for any two nonempty subsets X and Y of V.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 80EQ
Question
1: Prove the directed version of Veblen's Theorem : A directed graph admits a decomposition into directed cycles if and only if its even.
2: Show that a graph G is connected if and only if there is an (X,Y) - path in G for any two nonempty subsets X and Y of V.
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