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Prove that any graph with the degree sequence 2,5, 5, 7, 7, 7, 7, 7, 7 is Hamiltonian.

Prove that any graph with the degree sequence 2,5, 5, 7, 7, 7, 7, 7, 7 is Hamiltonian.

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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Prove that any graph with the degree sequence 2,5, 5, 7, 7, 7,7, 7, 7 is Hamiltonian. A complete tripartite graph is formed by taking three groups of vertices A, B, and C, then adding an edge between every pair of vertices in different groups. We write Kabe for the complete tripartite graph with |A| = a, |B| = b, and |C| = c. For example, below are diagrams of K2,4,5 (left) and K23,6 (right). (a) One of these graphs is Hamiltonian. Find a Hamiltonian cycle in that graph. (b) The other of these graphs is not Hamiltonian. Give a reason why it does not have a Hamiltonian cycle. (c) Generalize: find and prove a rule that tells you when Kabe is Hamiltonian. You may assume a <bSc.
Transcribed Image Text:Prove that any graph with the degree sequence 2,5, 5, 7, 7, 7,7, 7, 7 is Hamiltonian. A complete tripartite graph is formed by taking three groups of vertices A, B, and C, then adding an edge between every pair of vertices in different groups. We write Kabe for the complete tripartite graph with |A| = a, |B| = b, and |C| = c. For example, below are diagrams of K2,4,5 (left) and K23,6 (right). (a) One of these graphs is Hamiltonian. Find a Hamiltonian cycle in that graph. (b) The other of these graphs is not Hamiltonian. Give a reason why it does not have a Hamiltonian cycle. (c) Generalize: find and prove a rule that tells you when Kabe is Hamiltonian. You may assume a <bSc.
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