Edge cover by bipartite subgraphs
نویسندگان
چکیده
k≤m Ek and m is minimum. Two related and reasonably well-studied problems are the Minimum Biclique Cover (MBC), where Hk are required to be bicliques (i.e. complete bipartite subgraphs) [4,3,2,1] and the Minimum Cut Cover (MCC), where Hk are cutsets, namely not required to be connected. Both problems are NP-hard. To the best of our knowledge, whether the MBGC is NP-hard or not is currently unknown. Let G = (V,E) be an undirected graph. For v ∈ V , we denote by δ(v) the set of vertices u such that {v, u} ∈ E, and by δ̄(v) the set of edges e ∈ E adjacent to v. With respect to a set of edges F ⊂ E, δF (v) is the set of vertices adjacent to v using edges in F , and δ̄F (v) is the set of edges e ∈ F adjacent to v.
منابع مشابه
Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite Graphs
A bipartite graph G = (U, V,E) is convex if the vertices in V can be linearly ordered such that for each vertex u ∈ U , the neighbors of u are consecutive in the ordering of V . An induced matching H of G is a matching such that no edge of E connects endpoints of two different edges of H. We show that in a convex bipartite graph with n vertices and m weighted edges, an induced matching of maxim...
متن کاملCovering Graphs with Few Complete Bipartite Subgraphs
We consider computational problems on covering graphs with bicliques (complete bipartite subgraphs). Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the graph can be covered with at most k bicliques; the biclique partition problem is defined similarly with the additional condition that the bicliques are required to be mutually edge-disjoint. The biclique ...
متن کاملOrthogonal double covers of complete bipartite graphs
Let H = {A1, . . . , An, B1, . . . , Bn} be a collection of 2n subgraphs of the complete bipartite graph Kn,n. The collection H is called an orthogonal double cover (ODC) of Kn,n if each edge of Kn,n occurs in exactly two of the graphs in H; E(Ai) ∩ E(Aj) = φ = E(Bi) ∩ E(Bj) for every i, j ∈ {1, . . . , n} with i = j, and for any i, j ∈ {1, . . . , n}, |E(Ai)∩E(Bj)| = 1. If Ai ∼= G ∼= Bi for al...
متن کاملOrthogonal double covers of complete bipartite graphs by the union of a cycle and a star
Abstract Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex. Then G is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of G and any two members of G share exactly an edge whenever the corresponding vertices are adjacent in H. If all subgraphs in G are isomorphic to a given spanning subgraph G, then G is said to be an...
متن کاملBipartite decomposition of random graphs
Definition (Maximal size complete bipartite induced subgraph). β(G) := size of maximal complete bipartite induced subgraph of G. Definition (Minimal bipartite decomposion number). τ(G) := minimal number of complete edge disjoint covering bipartite subgraphs of G. Definition (Minimal nontrivial bipartite decomposion number). τ (G) := minimal number of complete edge disjoint covering nontrivial (...
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 2007