Math Problem Statement
Let G be a graph with order n ≥ 3. Let u and v be distinct nonadjacent vertices of G such that deg(u) + deg(v) ≥ n. Let G + uv be the graph obtained from G by adding the edge uv joining u and v. Using cycle exchanges, prove the following statement: If G + uv is Hamiltonian, then so is G.
Solution
Math Problem Analysis
Mathematical Concepts
Graph Theory
Hamiltonian Cycle
Vertex Degrees
Formulas

Theorems
Hamiltonian Cycle Theorem
Suitable Grade Level
Advanced Undergraduate
Related Recommendation
Proof that Bipartite Graphs of Odd Order Are Not Hamiltonian
Prove Inequality Involving Chromatic Numbers in Graph Theory
Prove that a Graph G is 2Connected Given Hamiltonian Path Property
Prove NonHamiltonian Property of K_{r, 2r, 3r+1} Graph
Prove that Kr, 2r, 3r is Hamiltonian for any positive integer r