Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Stable sets in certain P6-free graphs
Discrete Applied Mathematics
The complexity of coloring graphs without long induced paths
Acta Cybernetica
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the stable set problem in special P5-free graphs
Discrete Applied Mathematics
3-Colorability ∈ P for P6-free graphs
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Solving Connected Dominating Set Faster than 2 n
Algorithmica - Parameterized and Exact Algorithms
A new characterization of P6-free graphs
Discrete Applied Mathematics
On Partitioning a Graph into Two Connected Subgraphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On partitioning a graph into two connected subgraphs
Theoretical Computer Science
Removing local extrema from imprecise terrains
Computational Geometry: Theory and Applications
Increasing the minimum degree of a graph by contractions
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Solving the 2-disjoint connected subgraphs problem faster than 2n
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
| Hi-index | 5.23 |
The 2-Disjoint Connected Subgraphs problem asks if a given graph has two vertex-disjoint connected subgraphs containing prespecified sets of vertices. We show that this problem is NP-complete even if one of the sets has cardinality 2. The Longest Path Contractibility problem asks for the largest integer @? for which an input graph can be contracted to the path P"@? on @? vertices. We show that the computational complexity of the Longest Path Contractibility problem restricted to P"@?-free graphs jumps from being polynomially solvable to being NP-hard at @?=6, while this jump occurs at @?=5 for the 2-Disjoint Connected Subgraphs problem. We also present an exact algorithm that solves the 2-Disjoint Connected Subgraphs problem faster than O^*(2^n) for any n-vertex P"@?-free graph. For @?=6, its running time is O^*(1.5790^n). We modify this algorithm to solve the Longest Path Contractibility problem for P"6-free graphs in O^*(1.5790^n) time.