Corollary 11.6: If G = (V,E) is a loop-free undirected graph with |V| = n ≥ 3, and if |E| ≥ ("₂¹) +2, then G has a Hamilton cycle.
Corollary 11.6: If G = (V,E) is a loop-free undirected graph with |V| = n ≥ 3, and if |E| ≥ ("₂¹) +2, then G has a Hamilton cycle.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
Problem 23EQ
Related questions
Question
4. Let n ∈ Z+ with n ≥ 4, and let the vertex set V ′ for the complete graph Kn−1 be
{v1, v2, v3, . . . , vn−1}. Now construct the loop-free undirected graph Gn = (V, E) from Kn−1 as
follows: V = V ′ ∪ {v}, and E consists of all the edges in Kn−1 except for the edge {v1, v2}, which
is replaced by the pair of edges {v1, v} and {v, v2}.
a) Determine deg(x) + deg(y) for all nonadjacent vertices x and y in V .
b) Does Gn have a Hamilton cycle?
c) How large is the edge set E?
d) Do the results in parts (b) and (c) contradict Corollary 11.6?
Transcribed Image Text:Corollary 11.6: If G = (V,E) is a loop-free undirected graph with |V| = n ≥ 3, and if
|E| ≥ ("₂¹) +2, then G has a Hamilton cycle.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 6 images
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning