Paper Info
Title
A covering problem that is easy for trees but I-complete for trivalent graphs
Abstract
By definition, a P2-graph Γ is an undirected graph in which every vertex is contained in a path of length two. For such a graph, pc(Γ) denotes the minimum number of paths of length two that cover all n vertices of Γ. We prove that ⌈n/3⌉≤pc(Γ)≤⌊n/2⌋ and show that these upper and lower bounds are tight. Furthermore we show that every connected P2-graph Γ contains a spanning tree T such that pc(Γ)=pc(T). We present a linear time algorithm that produces optimal 2-path covers for trees. This is contrasted by the result that the decision problem pc(Γ)=?n/3 is NP-complete for trivalent graphs. This graph theoretical problem originates from the task of searching a large database of biological molecules such as the Protein Data Bank (PDB) by content.
Year
DOI
Venue
2008
10.1016/j.dam.2007.11.021
Discrete Applied Mathematics
Keywords
DocType
Volume
Covering problems,2-path cover,Edge cover,Optimal tree cover,Tiling problems,Trivalent graphs
Journal
156
Issue
ISSN
Citations 
15
0166-218X
0
PageRank 
References 
Authors
0.34
3
3
Name
Order
Citations
PageRank
Rolf Bardeli1698.09
Michael Clausen246943.66
Andreas Ribbrock3162.46