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Let G be a bipartite groph with graph X and Y. Suppose that for every parts X seX, N(S)|> (sl-d for some for Some integer d>o. Prove that a has a mat ching with at least X-d edges.

Let G be a bipartite groph with graph X and Y. Suppose that for every parts X seX, N(S)|> (sl-d for some for Some integer d>o. Prove that a has a mat ching with at least X-d edges.

Database System Concepts
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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(Graph Theory)
2. Let \( G \) be a bipartite graph with parts \( X \) and \( Y \). Suppose that for every \( S \subseteq X \), \(|N(S)| \geq |S| - d\) for some integer \( d \geq 0 \). Prove that \( G \) has a matching with at least \(|X| - d\) edges.
Transcribed Image Text:2. Let \( G \) be a bipartite graph with parts \( X \) and \( Y \). Suppose that for every \( S \subseteq X \), \(|N(S)| \geq |S| - d\) for some integer \( d \geq 0 \). Prove that \( G \) has a matching with at least \(|X| - d\) edges.
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