Hi SageMath community,

My name is Muhammet, and I am an undergraduate student with a strong 
interest in Graph Theory and algorithms. I am writing to express my 
enthusiasm for contributing to SageMath as part of *GSoC 2026*.

Recently, I developed an *Exact Planarity Solver* entirely from scratch in 
Python. The project implements planarity testing based on *rotation systems* 
and concepts inspired by the *Boyer–Myrvold algorithm*, without relying on 
external graph libraries. The focus was on correctness, explicit handling 
of edge cases, and clarity of the underlying mathematical logic.

*Live demo:* https://interactive-planarity-solver-dogukanv2.streamlit.app
*Repository:* https://github.com/ProfTR55/interactive-planarity-solver

I initially shared this work with the NetworkX team, where it received 
encouraging feedback (e.g., “The Streamlit app looks nice!”). Although 
NetworkX is not participating in GSoC this year, the experience motivated 
me to look for organizations with a strong emphasis on exact mathematical 
computation and rigor, which naturally led me to SageMath.  

Given SageMath’s role as a leading open-source platform for mathematical 
software, I believe my background and interests align well with the goals 
of the project—especially within the sage.graphs module.

*My technical background includes:*

   - 
   
   *Domain:* Graph Theory, Combinatorics, Planarity Testing
   - 
   
   *Languages:* Python (algorithm design and prototyping), C++ 
   (performance-oriented implementations)
   
I am especially interested in using my *C++ experience* to optimize 
performance-critical graph algorithms in SageMath, or to contribute to 
improvements in graph drawing and visualization.

I would greatly appreciate any guidance on potential GSoC project ideas in 
this area, or pointers to suitable *“good first issues”* where I could 
start contributing and familiarizing myself with the codebase.

Thank you for your time and for maintaining such an impactful project.

Best regards,
Muhammet

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