Consider a simple graph with 9 vertices, such that the degree of each vertex is either 5 or 6. Prove that there are at least 5 vertices of degree 6 or at least 6 vertices of degree 5.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
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1. Let the degree sequence of a graph G be the sequence of length |V(G)| that contains
the degrees of the vertices of G in non-increasing order.
(b) Consider a simple graph with 9 vertices, such that the degree of each vertex is
either 5 or 6. Prove that there are at least 5 vertices of degree 6 or at least 6
vertices of degree 5.
Transcribed Image Text:1. Let the degree sequence of a graph G be the sequence of length |V(G)| that contains the degrees of the vertices of G in non-increasing order. (b) Consider a simple graph with 9 vertices, such that the degree of each vertex is either 5 or 6. Prove that there are at least 5 vertices of degree 6 or at least 6 vertices of degree 5.
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