On Partial Vertex Cover on Bipartite Graphs and Trees

Bugra Caskurlu; K. Subramani

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arXiv · 1304.5934

On Partial Vertex Cover on Bipartite Graphs and Trees

Bugra Caskurlu·K. Subramani

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Abstract

It is well-known that the Vertex Cover problem is in P on bipartite graphs, however; the computational complexity of the Partial Vertex Cover problem on bipartite graphs is open. In this paper, we first show that the Partial Vertex Cover problem is NP-hard on bipartite graphs. We then identify an interesting special case of bipartite graphs, for which the Partial Vertex Cover problem can be solved in polynomial-time. We also show that the set of acyclic bipartite graphs, i.e., forests, and the set of bipartite graph where the degree of each vertex is at most 3 fall into that special case. Therefore, we prove that the Partial Vertex Cover problem is in P on trees, and it is also in P on the set of bipartite graphs where the degree of each vertex is at most 3.

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Bugra Caskurlu, K. Subramani. 2013-04-22. On Partial Vertex Cover on Bipartite Graphs and Trees. https://arxiv.org/abs/1304.5934

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