Some results on graphs without long induced paths
Information Processing Letters
NP-hard graph problems and boundary classes of graphs
Theoretical Computer Science
A factor 2 approximation algorithm for the vertex cover P3 problem
Information Processing Letters
Discrete Applied Mathematics
On computing the minimum 3-path vertex cover and dissociation number of graphs
Theoretical Computer Science
Design and analysis of a generalized canvas protocol
WISTP'10 Proceedings of the 4th IFIP WG 11.2 international conference on Information Security Theory and Practices: security and Privacy of Pervasive Systems and Smart Devices
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A subset S of vertices of a graph G is called a vertex k-path cover if every path of order k in G contains at least one vertex from S. Denote by @j"k(G) the minimum cardinality of a vertex k-path cover in G. In this paper, an upper bound for @j"3 in graphs with a given average degree is presented. A lower bound for @j"k of regular graphs is also proven. For grids, i.e. the Cartesian products of two paths, we give an asymptotically tight bound for @j"k and the exact value for @j"3.