A linear algorithm for bipartition of biconnected graphs
Information Processing Letters
A linear-time algorithm for four-partitioning four-connected planar graphs
Information Processing Letters
Decomposable trees: a polynomial algorithm for tripodes
Discrete Applied Mathematics
On minimal arbitrarily partitionable graphs
Information Processing Letters
Note: Partitioning powers of traceable or hamiltonian graphs
Theoretical Computer Science
| Hi-index | 5.23 |
An n-vertex graph is said to be decomposable for a partition (@l"1,...,@l"p) of the integer n if there exists a sequence (V"1,...,V"p) of connected vertex-disjoint subgraphs with |V"i|=@l"i. An n-vertex graph is said to be decomposable if this graph is decomposable for all the partitions of the integer n. We are interested in decomposable trees with large diameter. We show that any n-vertex tree T with diameter n-@a is decomposable for all the partitions of n which contain at least @a distinct integers. This structural result provides an algorithm to decide if an n-vertex tree T with diameter n-@a is decomposable in time n^O^(^@a^).