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Title: | On the Complexity of the K-way Vertex Cut Problem |
Authors: | LALOU, Mohammed |
Keywords: | Vertex separator critical nodes graph connec- tivity bipartite graphs split graphs NP-completeness |
Issue Date: | 4-Mar-2019 |
Publisher: | Université Kasdi Merbah Ouargla |
Series/Report no.: | 2019; |
Abstract: | The K-way vertex cut problem consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It has been proven to be NP-complete on general graphs, as well as on split and planar graphs. In this paper, we enrich its complexity study with two new results. First, we prove that it remains NP-complete even when restricted on the class of bipartite graphs. This is unlike what it is expected, given that the K-way vertex cut problem is a generalization of the Maximum Independent set problem which is polynomially solvable on bipartite graphs. We also provide its equivalence to the well- known problem, namely the Critical Node Problem (CNP), On split graphs. Therefore, any solving algorithm for the CNP on split graphs is a solving algorithm for the K-way vertex cut problem and vice versa. |
Description: | Le 2eme Conference Internationale sur intelligence Artificielle et les Technologies Information ICAIIT 2019 |
URI: | http://dspace.univ-ouargla.dz/jspui/handle/123456789/20859 |
Appears in Collections: | 2. Faculté des nouvelles technologies de l’information et de la communication |
Files in This Item:
File | Description | Size | Format | |
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Mohammed LALOU.pdf | 567,09 kB | Adobe PDF | View/Open |
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