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In the fractional set cover problem, it is allowed to select fractions of sets, rather than entire sets. A fractional set cover is an assignment of a fraction (a number in [0,1]) to each set in , such that for each element x in the universe, the sum of fractions of sets that contain x is at least 1. The goal is to find a fractional set cover in ...
Conflict-free set cover is the problem of finding a conflict-free subset of O that is a covering of P. Banik, Panolan, Raman, Sahlot and Saurabh [ 7 ] prove the following for the special case in which the conflict-graph has bounded arboricity :
In the mathematical discipline of graph theory, a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to the vertex set of G. A covering map f is a surjection and a local isomorphism: the neighbourhood of a vertex v in C is mapped bijectively onto the neighbourhood of in G. The term lift is ...
Example graph that has a vertex cover comprising 2 vertices (bottom), but none with fewer. In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem.
A vertex-cover (aka hitting set or transversal) in H is set T ⊆ V such that, for all hyperedges e ∈ E, it holds that T ∩ e ≠ ∅. The vertex-cover number (aka transversal number) of a hypergraph H is the smallest size of a vertex cover in H. It is often denoted by τ(H). [1]: 466 For example, if H is this 3-uniform hypergraph:
The Hasse diagram depicting the covering relation of a Tamari lattice is the skeleton of an associahedron. The covering relation of any finite distributive lattice forms a median graph. On the real numbers with the usual total order ≤, the cover set is empty: no number covers another.
The set C is said to cover the vertices of G. The following figure shows examples of edge coverings in two graphs (the set C is marked with red). A minimum edge covering is an edge covering of smallest possible size. The edge covering number ρ(G) is the size of a minimum edge covering.
A set of cliques that cover all edges of a graph is called a clique edge cover [3] or edge clique cover, [4] or even just a clique cover, although the last term is ambiguous: a clique cover can also be a set of cliques that cover all vertices of a graph. [5] Sometimes "covering" is used in place of "cover". [6] As well as being called the ...