please write out equations and explain/write out theorems **Problem 2:** Let \( G \) and \( H \) be the graphs below. For each graph, determine whether it is bipartite. If the graph is bipartite, determine whether it has a perfect matching. Justify your answer.**Graph \( G \):**- **Vertices**: \( c, i, b, e, d, g, f \)- **Edges**: The connections between vertices are as follows: - \( c \) is connected to \( g \) and \( i \). - \( i \) is connected to \( b \) and \( e \). - \( e \) is connected to \( f \). - \( d \) has edges connecting to \( c \), \( e \), and \( g \). - \( g \) is also connected to \( f \). The graph forms a structure where edges create interconnected pathways among seven vertices.**Graph \( H \):**- **Vertices**: \( b, a, j, g, f, d, c, i, e, h \)- **Edges**: The connections between vertices are as follows: - \( b \) is connected to \( g \) and \( a \). - \( a \) is connected to \( j \). - \( j \) is connected to \( g \) and \( h \). - \( h \) is connected to \( c \). - \( g \) connects \( i \), which also connects to \( c \). - \( f \) is connected to \( e \). - \( d \) connects to \( b, c, \) and \( i \).The graph demonstrates a more complex network with multiple connections forming paths and cycles between ten vertices.

Answered: Image /qna-images/answer/e520257f-8c36-46b1-88a1-a38e8f4c51b5.jpg

Problem 2: Let G and H be the graphs below. For each graph, determine whether it is bipartite. If the graph is bipartite, determine whether it has a perfect matching. Justify your answer. Graph G: Graph H:

Problem 2: Let G and H be the graphs below. For each graph, determine whether it is bipartite. If the graph is bipartite, determine whether it has a perfect matching. Justify your answer. Graph G: Graph H:

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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