My First Research Paper on Hamiltonian Cycles

Hello everyone! Today marks the beginning of my first research paper journey. I'm incredibly excited to dive into this project, which I have an entire year to complete. This is a fantastic opportunity for me to contribute to the field of mathematics, a subject that I'm deeply passionate about.

What is it about?

My research will focus on Hamiltonian Cycles in Graph Theory. For those who might not be familiar, a Hamiltonian Cycle in a graph is a cycle that visits each vertex exactly once and returns to the starting vertex. This is a classic problem in graph theory with numerous applications in computer science, operations research, and even real-world problems like the Traveling Salesman Problem.

Why Hamiltonian Cycles?

I chose this topic because:

1. It's a fundamental problem in graph theory
2. It has practical applications in various fields
3. It's mathematically beautiful and challenging
4. There are still many open questions and research opportunities

My Approach

Over the next year, I plan to:

1. Conduct a thorough literature review of existing research
2. Explore different algorithms for finding Hamiltonian cycles
3. Investigate properties of graphs that guarantee Hamiltonian cycles
4. Look for new patterns and connections in graph theory

Challenges Ahead

I anticipate several challenges:

• The computational complexity of the problem
• Finding innovative approaches to existing problems
• Balancing theoretical insights with practical applications
• Ensuring my research contributes meaningfully to the field

Next Steps

I'll be documenting my progress regularly on this blog. Stay tuned for updates on:

• Research methodology
• Interesting findings
• Challenges and solutions
• Progress milestones

This is just the beginning of what I hope will be an exciting and rewarding journey. I'm looking forward to sharing more about my research in future posts!