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August 13, 2026Open Access

Completing the Boundary Case of the Mahmoodian–Mirzakhani Conjecture and 117 New Computational 5-Cycle Decompositions of Complete Tripartite Graphs

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RPRoozbeh Pournader

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Overview

Randomized trial explores exhaustive cycle decompositions in complete tripartite graphs, implying resolution of a conjecture.

Key Points

  • This study aims to prove the Mahmoodian–Mirzakhani conjecture for specific tripartite graphs and report new computational results.
  • Constructive proof addressing the extremal boundary condition t = 4rs/(r + s) for odd triples.
  • Generation of 117 new cycle decompositions using computational methods and existing theoretical frameworks.
  • Use of exact-cover search to obtain machine-readable cycle-list certificates.
  • Proved the conjecture for all odd triples on the boundary condition with t = 4rs/(r + s).
  • Generated and verified 117 new C5-decompositions, resolving previously unresolved cases under specific edge conditions.
  • All computational results archived in a Zenodo record for independent verification.

Cite This Study

Roozbeh Pournader (2026) studied this question.

synapsesocial.com/papers/6a7d76e62b0e0cff3f640a33https://doi.org/10.5281/zenodo.21882726
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