On a relation between k-path partition and k-path vertex cover
نویسندگان
چکیده
The vertex cover problem and the vertex partition problem are central problems in graph theory and many generalizations are known. Two examples are the minimum k-path vertex cover problem (MkPVCP for short, introduced in [1]), which asks for a minimum vertex sets covering every path of length k−1, and the minimum k-path partition problem (MkPPP for short, introduced in [2]), which asks for a minimum number of paths in a maximal path packing whose every path has at least one and at most k vertices. In this talk we will present a relation between MkPPP and MkPVCP, which gives us new bounds for their invariants and a new necessary condition for NP-hardness of MkPVCP in terms of forbidden subgraphs.
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عنوان ژورنال:
- Discrete Applied Mathematics
دوره 223 شماره
صفحات -
تاریخ انتشار 2017