On the complete width and edge clique cover problems
نویسندگان
چکیده
منابع مشابه
On the Complete Width and Edge Clique Cover Problems
A complete graph is the graph in which every two vertices are adjacent. For a graph G = (V,E), the complete width of G is the minimum k such that there exist k independent sets Ni ⊆ V , 1 ≤ i ≤ k, such that the graph G obtained from G by adding some new edges between certain vertices inside the sets Ni, 1 ≤ i ≤ k, is a complete graph. The complete width problem is to decide whether the complete...
متن کاملClique-width and edge contraction
We prove that edge contractions do not preserve the property that a set of graphs has bounded clique-width.
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Clique-width is a graph parameter that measures in a certain sense the complexity of a graph. Hard graph problems (e.g., problems expressible in Monadic Second Order Logic with second-order quantification on vertex sets, that includes NP-hard problems such as 3-colorability) can be solved in polynomial time for graphs of bounded clique-width. We show that the clique-width of a given graph canno...
متن کاملUnit Incomparability Dimension and Clique Cover Width in Graphs
For a clique cover C in the undirected graph G, the clique cover graph of C is the graph obtained by contracting the vertices of each clique in C into a single vertex. The clique cover width of G, denoted by CCW (G), is the minimum value of the bandwidth of all clique cover graphs in G. Any G with CCW (G) = 1 is known to be an incomparability graph, and hence is called, a unit incomparability g...
متن کاملKnown algorithms for EDGE CLIQUE COVER are probably optimal
In the EDGE CLIQUE COVER (ECC) problem, given a graph G and an integer k, we ask whether the edges of G can be covered with k complete subgraphs of G or, equivalently, whether G admits an intersection model on k-element universe. Gramm et al. [JEA 2008] have shown a set of simple rules that reduce the number of vertices of G to 2, and no algorithm is known with significantly better running time...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2016
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-016-0106-9