In the mathematical fields of graph theory and combinatorial optimization, the bipartite dimension or biclique cover number of a graph G = (V, E) is the minimum number of bicliques (that is complete bipartite subgraphs), needed to cover all edges in E. A collection of bicliques covering all edges in G is called a biclique edge cover, or sometimes biclique cover. The bipartite dimension of G is often denoted by the symbol d(G).
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optimization, the bipartitedimension or biclique cover number of a graph G = (V, E) is the minimum number of bicliques (that is complete bipartite subgraphs)...
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets...
of bipartitedimension (of the complemented bipartite graph) translates to that of Ferrers dimension (of the formal context) and of order dimension (of...
The minimum number of complete bipartite subgraphs needed to cover the edges of a crown graph (its bipartitedimension, or the size of a minimum biclique...
The chromatic number of the dimension-k folded cube graph is two when k is even (that is, in this case, the graph is bipartite) and four when k is odd. The...
a problem in topological graph theory by asking whether the complete bipartite graph K 3 , 3 {\displaystyle K_{3,3}} , with vertices representing the...
state is a d 2 {\displaystyle d^{2}} × d 2 {\displaystyle d^{2}} -dimensionalbipartite quantum state density matrix that is invariant under all unitary...
computer networking Complete bipartite graph (or biclique), a special bipartite graph where every vertex on one side of the bipartition is connected to every...
{\frac {n(n+1)}{2}}} , then the n-dimensional cube Qn has an interval t-coloring. For any m, n ∈ N, the complete bipartite graph Km,n is interval colorable...
of bipartite graphs are perfect. Examples include the rook's graphs, the line graphs of complete bipartite graphs. Every line graph of a bipartite graph...
does not contain a subgraph that is a subdivision of K5, or the complete bipartite utility graph K3,3. A similar graph is the Petersen graph, which is strongly...
example is a special case of the following general theorem:: 274 G is a bipartite graph if-and-only-if MP(G) = FMP(G) if-and-only-if all corners of FMP(G)...
in bipartite graphs. Degree matrix — a diagonal matrix defining the degree of each vertex in a graph. Edmonds matrix — a square matrix of a bipartite graph...
portrayed as being equivalent to entanglement. While this is true for pure bipartite quantum states, in general entanglement is only necessary for non-local...
K_{6}} K 7 {\displaystyle K_{7}} K 8 {\displaystyle K_{8}} The complete bipartite graph is usually denoted K n , m {\displaystyle K_{n,m}} . For n = 1 {\displaystyle...
interpretation. Suppose V {\displaystyle V} , W {\displaystyle W} are finite-dimensional vector spaces over a field, with dimensions m {\displaystyle m} and n...
their connection to graph theory: bipartite Cayley graphs over any subset of a quasirandom group are always bipartite quasirandom graphs. The notion of...
characteristic dynamic length scales for protein functionality. The fractal dimension can be calculated using methods such as the box counting method or the...
Consider first composite states with two degrees of freedom, referred to as bipartite states. By a postulate of quantum mechanics these can be described as...
entanglement was discovered by M. Horodecki, P. Horodecki, and R. Horodecki. Bipartite entangled states that have a non-negative partial transpose are all bound-entangled...
equivalent to an exact hitting set problem, an incidence matrix, or a bipartite graph. In computer science, the exact cover problem is a decision problem...
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