On the rotation distance in the lattice of binary trees
Information Processing Letters
Guthrie's problem: new equivalences and rapid reductions
ICALP Selected papers of the twentieth international colloquium on Automata, languages and programming
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Twist-rotation transformations of binary trees and arithmetic expressions
Journal of Algorithms
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Theoretical Computer Science
Note: Refined upper bounds for right-arm rotation distances
Theoretical Computer Science
A metric for rooted trees with unlabeled vertices based on nested parentheses
Theoretical Computer Science
Hi-index | 5.23 |
The famous four-colour problem of planar maps is equivalent, by an optimally fast reduction, to the problem of colouring pairs of binary trees (CPBT). Extant proofs of the four colour theorem lack conciseness, are not lucid in their detail and require hours of electronic computation. The search for a more satisfactory proof continues and, in this spirit, we explore one approach to CPBT based upon the rotation operation in binary trees. We prove that a more satisfactory proof exists if a rotational path between the two trees of every problem instance satisfies our non-colour-clashing sequence conjecture.