Graceful Graphs
Problem Description
A graph (V,E) is called a graceful graph if its vertices V can be labelled with distinct unsigned integers, its edges E can be labelled with the absolute differences between vertex labels, and the edge labels are in the range {1..|E|}. The task is to determine the existence of a graceful labelling of a graph.
The edges of the graph are provided by instances of the predicate edge/2. If a graceful labelling exists, a witness containing vertex labels encoded in the predicate value/2 has to be provided. value(X,I) means the vertex X is labelled with the unsigned integer I.
Predicates
Input: edge/2
Output: value/2
Input format
Output format
Example(s)
Problem Peculiarities
Type: Search Competition: Both Complexity: NP
Notes and Updates
Author(s)
- Author: Christian Drescher
- Affiliation: NICTA, University of New South Wales, Australia