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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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?
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
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,