ibelgin

To prove that every ( k )-regular graph on ( 2k + 1 ) vertices is Hamiltonian, we’ll use some concepts and arguments from graph theory. A ( k )-regular graph means that every vertex has exactly ( k ) edges.

Here's how we can approach the proof step-by-step:

Key Definitions and Theorem

1. ( k )-regular Graph: A graph where every vertex has exactly ( k ) edges.
2. Number of Vertices: ( 2k + 1 ) vertices.
3. Hamiltonian Cycle: A cycle that visits each vertex exactly once and returns to the starting vertex.

ibelgin

Linked List Optimization Research

Key Focus Areas

1. Cache-optimized traversal
2. Batch insertion patterns
3. Memory pool allocation
4. Performance measurement infrastructure

Complete Runnable Code