On the Complexity Landscape of Connected f -Factor Problems

R. Ganian; N. S. Narayanaswamy; S. Ordyniak; C. S. Rahul; M. S. Ramanujan

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arXiv · 1812.02037

On the Complexity Landscape of Connected f -Factor Problems

R. Ganian·N. S. Narayanaswamy·S. Ordyniak·C. S. Rahul·M. S. Ramanujan

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Abstract

Let G be an undirected simple graph having n vertices and let f be a function defined to be f:V(G) -> {0,..., n-1}. An f-factor of G is a spanning subgraph H such that degree of a vertex v in H is f(v) for every vertex v in V(G). The subgraph H is called a connected f-factor if, in addition, H is connected. A classical result of Tutte(1954) is the polynomial time algorithm to check whether a given graph has a specified f-factor. However, checking for the presence of a connected f-factor is easily seen to generalize HAMILTONIAN CYCLE and hence is NP-complete. In fact, the CONNECTED f-FACTOR problem remains NP-complete even when we restrict f(v) to be at least n^e for each vertex v and 0 1, the problem is NP-intermediate.

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R. Ganian, N. S. Narayanaswamy, S. Ordyniak, C. S. Rahul, M. S. Ramanujan. 2018-12-05. On the Complexity Landscape of Connected f -Factor Problems. https://arxiv.org/abs/1812.02037

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