1. A tournament on n vertices is a complete directed graph; that is, for any two distinct vertices æ and y either there is an edge from a to y, or there is an edge from y to a, but not both. (a) A directed path that visits every vertex once is called a directed Hamilton path. Prove that every tournament on n vertices has a directed Hamilton path. Hint: try induction on n by constructing a longer directed Hamilton path from the shorter one. (b) Devise an efficient algorithm to find a Hamilton path in a tournament and analyze its running time.

1. A tournament on n vertices is a complete directed graph; that is, for any two distinct vertices æ and y either there is an edge from a to y, or there is an edge from y to a, but not both. (a) A directed path that visits every vertex once is called a directed Hamilton path. Prove that every tournament on n vertices has a directed Hamilton path. Hint: try induction on n by constructing a longer directed Hamilton path from the shorter one. (b) Devise an efficient algorithm to find a Hamilton path in a tournament and analyze its running time.

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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Question

Part a) only please

1. A tournament on n vertices is a complete directed graph; that is, for any two distinct vertices
x and y either there is an edge from z to y, or there is an edge from y to a, but not both.
(a) A directed path that visits every vertex once is called a directed Hamilton path. Prove
that every tournament on n vertices has a directed Hamilton path.
Hint: try induction on n by constructing a longer directed Hamilton path from the
shorter one.
(b) Devise an efficient algorithm to find a Hamilton path in a tournament and analyze its
running time.

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