On Total Vertex Cover Problem in Subcubic Graphs
نویسندگان
چکیده
A total vertex cover is a vertex cover whose induced subgraph consists of a set of connected components, each of which contains at least two vertices. The total vertex cover (TVC) problem ask for the total vertex cover with minimum cardinality. In this paper, we first show that the TVC problem is NP-complete for connected subcubic grid graphs of arbitrary large girth. Next, we show that the TVC problem is NP-complete for 3-connected cubic planar graphs. Moreover, we show that the TVC problem is APX-complete for connected subcubic graphs of arbitrary large girth.
منابع مشابه
Coloring Algorithms on Subcubic Graphs
We present efficient algorithms for three coloring problems on subcubic graphs. (A subcubic graph has maximum degree at most three.) The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring. Our algorithm runs in linear time, and appears to be simpler than previous ones. The second algorithm is the first randomized EREW PRAM algorithm for the same problem. It uses O(n...
متن کاملA Note on Irreversible 2-Conversion Sets in Subcubic Graphs
Irreversible k-conversion set is introduced in connection with the mathematical modeling of the spread of diseases or opinions. We show that the problem to find a minimum irreversible 2-conversion set can be solved in O(n2 log6 n) time for graphs with maximum degree at most 3 (subcubic graphs) by reducing it to the graphic matroid parity problem, where n is the number of vertices in a graph. Th...
متن کاملUpper Domination: Complexity and Approximation
We consider Upper Domination, the problem of finding a maximum cardinality minimal dominating set in a graph. We show that this problem does not admit an n1− approximation for any > 0, making it significantly harder than Dominating Set, while it remains hard even on severely restricted special cases, such as cubic graphs (APXhard), and planar subcubic graphs (NP-hard). We complement our negativ...
متن کاملOn the Maximum Independent Set Problem in Subclasses of Subcubic Graphs
It is known that the maximum independent set problem is NP-complete for subcubic graphs, i.e. graphs of vertex degree at most 3. Moreover, the problem is NP-complete for 3-regular Hamiltonian graphs and for H-free subcubic graphs whenever H contains a connected component which is not a tree with at most 3 leaves. We show that if every connected component of H is a tree with at most 3 leaves and...
متن کاملThe robust vertex centdian location problem with interval vertex weights on general graphs
In this paper, the robust vertex centdian location problem with uncertain vertex weights on general graphs is studied. The used criterion to solve the problem is the min-max regret criterion. This problem is investigated with objective function contains $lambda$ and a polynomial time algorithm for the problem is presented. It is shown that the vertex centdian problem on general graphs i...
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:
دوره شماره
صفحات -
تاریخ انتشار 2016