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
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Rotation sequences and edge-colouring of binary tree pairs
Theoretical Computer Science
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The famous Four-colour Problem (FCP) of planar maps is equivalent, byan optimallyfast reduction, to the problem of Colouring Pairs of Binary Trees (CPBT). Extant proofs of FCP lack conciseness, lucidityand require hours of electronic computation. The search for a satisfactorypro of continues and, in this spirit, we explore two approaches to CPBT. In the first, we prove that a satisfactorypro of exists if the rotational path between the two trees of the problem instance always satisfies a specific condition embodied in our Shortest Path Conjecture. In our second approach, we look for patterns of colourability within regular forms of tree pairs and seek to understand all instances of CPBT as a perturbation of these. In this Colouring Topologies approach, we prove, for instance, that concise proofs to CPBT exist for instances contained within manyinfinite-sized sets of trees.