Computer-assisted proof of Havel's conjecture on spanning trees of hypercubes for dimension five
Description
Ivan Havel in 1984 published a conjecture claiming that an arbitrary tree of maximum degree at most three on 2ⁿ vertices is a spanning tree of the 𝑛-dimensional hypercube iff its bipartition classes are of the same size. Four decades have passed and the problem is still open; the statement has been verified with computer assistance for 𝑛 ≤ 4 while for larger dimensions its validity is known only for several special cases. This dataset provides a machine-verifiable proof of the validity of Havel's conjecture for dimension 𝑛 = 5 . The submitted files contain the following: computed_solution – a file containing the proof of Havel's conjecture for dimension 5 program.zip – an archive containing the program used to compute this solution, along with its documentation, including a function that receives a tree on 2⁵ vertices satisfying the assumptions of the conjecture in graphwiz format and outputs the desired embedding
Files
Steps to reproduce
The computed_solution file was generated using the program provided in program.zip. To reproduce the output, run the following command: cabal run hypercubes.cabal compute-output 5 computed_solution To find the precomputed solution for a given tree in graphwiz format, use the following arguments: find-solution <dimensionOfTree> <inputFile.dot> <solutionOfAllFile> <responseFile.dot>
Institutions
- Univerzita Karlova