ITSITS

(IJCSAM) International Journal of Computing Science and Applied Mathematics(IJCSAM) International Journal of Computing Science and Applied Mathematics

Searching all possible solution and finding the minimum number of clues to make uniquely solvable puzzle always been a natural question for puzzle enthusiast. However, the attempt usually provide that as difficult task. In this paper, we attempt to search the solution of Kropki puzzle without dot clues given with graph theory approach, which resulted in some conjectures involving the planarity of graph and cyclicity of latin square.

The study demonstrates that for n ≥ 6, every n-ordered dotless kropki graph possesses a Hamiltonian cycle.Specifically, for n = 6, the puzzles solutions are limited to 1-cyclic and 5-cyclic forms.Furthermore, the research proposes conjectures regarding the relationship between graph planarity, cyclicity, and the existence of solutions for dotless Kropki puzzles.

Penelitian lebih lanjut dapat dilakukan untuk menguji validitas konjektur yang diajukan mengenai hubungan antara planaritas graf, siklisitas, dan keberadaan solusi untuk puzzle Kropki tanpa titik. Selain itu, eksplorasi algoritma yang lebih efisien untuk mencari solusi puzzle Kropki dengan ukuran yang lebih besar (n > 8) sangat diperlukan, mengingat kompleksitas komputasi yang meningkat secara eksponensial. Terakhir, studi komparatif dapat dilakukan dengan jenis puzzle Latin Square lainnya, seperti Sudoku atau Futoshiki, untuk mengidentifikasi pola umum dan perbedaan dalam pendekatan penyelesaiannya, serta mengembangkan metode penyelesaian yang lebih universal.

  1. [1201.0749] There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem. clue sudoku... arxiv.org/abs/1201.07491201 0749 There is no 16 Clue Sudoku Solving the Sudoku Minimum Number of Clues Problem clue sudoku arxiv abs 1201 0749
  2. New Sufficient Conditions for Hamiltonian Paths - Rahman - 2014 - The Scientific World Journal - Wiley... hindawi.com/journals/tswj/2014/743431New Sufficient Conditions for Hamiltonian Paths Rahman 2014 The Scientific World Journal Wiley hindawi journals tswj 2014 743431
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