Recall that a subgraph H of a graph G is proper if H + G. a) Prove that if a connected graph G is a tree, then no proper spanning subgraph of G is connected. b) [NOTE: Can be solved without having done part a)!] Now prove the converse: if G is a connected graph such that no proper spanning subgraph of G is connected, then G is a tree.
Recall that a subgraph H of a graph G is proper if H + G. a) Prove that if a connected graph G is a tree, then no proper spanning subgraph of G is connected. b) [NOTE: Can be solved without having done part a)!] Now prove the converse: if G is a connected graph such that no proper spanning subgraph of G is connected, then G is a tree.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![Recall that a subgraph H of a graph G is proper if H + G.
a) Prove that if a connected graph G is a tree, then no proper spanning subgraph of G is
connected.
b) [NOTE: Can be solved without having done part a)!] Now prove the converse: if G is a
connected graph such that no proper spanning subgraph of G is connected, then G is a tree.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd93f2b94-57d5-4fc5-8104-ee5d4a79ec01%2F2684461d-e802-4f63-a1e8-e125ffa0aa1d%2Fxxqmuub_processed.png&w=3840&q=75)
Transcribed Image Text:Recall that a subgraph H of a graph G is proper if H + G.
a) Prove that if a connected graph G is a tree, then no proper spanning subgraph of G is
connected.
b) [NOTE: Can be solved without having done part a)!] Now prove the converse: if G is a
connected graph such that no proper spanning subgraph of G is connected, then G is a tree.
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