The Parameterized Complexity of Graph Cyclability
نویسندگان
چکیده
The cyclability of a graph is the maximum integer k for which every k vertices lie on a cycle. The algorithmic version of the problem, given a graph G and a nonnegative integer k, decide whether the cyclability of G is at least k, is NP-hard. We study the parametrized complexity of this problem. We prove that this problem, parameterized by k, is co-W[1]-hard and that its does not admit a polynomial kernel on planar graphs, unless NP ⊆ co-NP/poly. On the positive side, we give an FPT algorithm for planar graphs that runs in time 2 O(k2 log k) ·n2. Our algorithm is based on a series of graph-theoretical results on cyclic linkages in planar graphs.
منابع مشابه
The Complexity of Finding Subgraphs Whose Matching Number Equals the Vertex Cover Number
The class of graphs where the size of a minimum vertex cover equals that of a maximum matching is known as König-Egerváry graphs. König-Egerváry graphs have been studied extensively from a graph theoretic point of view. In this paper, we introduce and study the algorithmic complexity of finding maximumKönig-Egerváry subgraphs of a given graph. More specifically, we look at the problem of findin...
متن کاملOn the Parallel Parameterized Complexity of the Graph Isomorphism Problem
In this paper, we study the parallel and the space complexity of the graph isomorphism problem (GI) for several parameterizations. Let H = {H1,H2, · · · ,Hl} be a finite set of graphs where |V (Hi)| ≤ d for all i and for some constant d. Let G be an H-free graph class i.e., none of the graphs G ∈ G contain any H ∈ H as an induced subgraph. We show that GI parameterized by vertex deletion distan...
متن کاملFixed Parameter Complexity of Distance Constrained Labeling and Uniform Channel Assignment Problems - (Extended Abstract)
We study the complexity of a group of distance-constrained graph labeling problems when parameterized by the neighborhood diversity (nd), which is a natural graph parameter between vertex cover and clique width. Neighborhood diversity has been used to generalize and speed up FPT algorithms previously parameterized by vertex cover, as is also demonstrated by our paper. We show that the Uniform C...
متن کاملSome lower bounds in parameterized ${\rm AC}^0$
We demonstrate some lower bounds for parameterized problems via parameterized classes corresponding to the classical AC. Among others, we derive such a lower bound for all fptapproximations of the parameterized clique problem and for a parameterized halting problem, which recently turned out to link problems of computational complexity, descriptive complexity, and proof theory. To show the firs...
متن کاملThe complexity of irredundant sets parameterized by size
An irredundant set of vertices V ′ ⊆ V in a graph G = (V,E) has the property that for every vertex u ∈ V ′, N(V ′ − {u}) is a proper subset of N(V ′). We investigate the parameterized complexity of determining whether a graph has an irredundant set of size k, where k is the parameter. The interest of this problem is that while most “k-element vertex set” problems are NP-complete, several are kn...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 31 شماره
صفحات -
تاریخ انتشار 2014