Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
427041 | Information Processing Letters | 2016 | 4 Pages |
Abstract
•Packing r-stars in a graph with no long induced paths.•Parameter is the number k of r-stars.•Linear-vertex kernel.•Conjecture for the general case.
Let integers r≥2r≥2 and d≥3d≥3 be fixed. Let GdGd be the set of graphs with no induced path on d vertices. We study the problem of packing k vertex-disjoint copies of K1,rK1,r (k≥2k≥2) into a graph G from parameterized preprocessing, i.e., kernelization, point of view. We show that every graph G∈GdG∈Gd can be reduced, in polynomial time, to a graph G′∈GdG′∈Gd with O(k)O(k) vertices such that G has at least k vertex-disjoint copies of K1,rK1,r if and only if G′G′ has. Such a result is known for arbitrary graphs G when r=2r=2 and we conjecture that it holds for every r≥2r≥2.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Florian Barbero, Gregory Gutin, Mark Jones, Bin Sheng, Anders Yeo,