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
Deciding k-Colorability of P 5-Free Graphs in Polynomial Time
Algorithmica - Including a Special Section on Genetic and Evolutionary Computation; Guest Editors: Benjamin Doerr, Frank Neumann and Ingo Wegener
A new characterization of P6-free graphs
Discrete Applied Mathematics
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The 2-Disjoint Connected Subgraphs problem asks if a given graph has two vertex-disjoint connected subgraphs containing pre-specified 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 ${\cal O}^*(2^n)$ for any n -vertex P *** -free graph. For ***= 6, its running time is ${\cal O}^*(1.5790^n)$. We modify this algorithm to solve the Longest Path Contractibility problem for P 6 -free graphs in ${\cal O}^*(1.5790^n)$ time.