A Parameterized Perspective on Packing Paths of Length Two

We study (vertex-disjoint) packings of paths of length two (i.e., of P2's) in graphs under a parameterized perspective. Starting from a maximal P2-packing P of size j we use extremal combinatorial arguments for determining how many vertices of P appear in some P2-packing of size (j + 1) (if it exists). We prove that one can 'reuse' 2.5j vertices. Based on a WIN-WIN approach, we build an algorithm which decides if a P2-packing of size at least k exists in a given graph in time O (2.4823k ).

• Type: Conference
• Year: 2008
• Where: COCOA
• Authors: Henning Fernau, Daniel Raible
• Keywords: COCOA 2008, Discrete Geometry, Extremal Combinatorial Arguments, Maximal P2-packing, Parameterized Perspective