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A complete bipartite graph with m = 5 and n = 3 The Heawood graph is bipartite.. 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 and , that is, every edge connects a vertex in to one in .
By formulating MAX-2-SAT as a problem of finding a cut (that is, a partition of the vertices into two subsets) maximizing the number of edges that have one endpoint in the first subset and one endpoint in the second, in a graph related to the implication graph, and applying semidefinite programming methods to this cut problem, it is possible to ...
A vertex-signed graph, sometimes called a marked graph, is a graph whose vertices are given signs. A circle is called consistent (but this is unrelated to logical consistency) or harmonious if the product of its vertex signs is positive, and inconsistent or inharmonious if the product is negative. There is no simple characterization of ...
For instance, #SAT on SAT instances whose treewidth is bounded by a constant can be performed in polynomial time. [11] Here, the treewidth can be the primal treewidth, dual treewidth, or incidence treewidth of the hypergraph associated to the SAT formula, whose vertices are the variables and where each clause is represented as a hyperedge.
Example of a planar SAT problem. The black edges correspond to non-inverted variables and the red edges correspond to inverted variables. In computer science, the planar 3-satisfiability problem (abbreviated PLANAR 3SAT or PL3SAT) is an extension of the classical Boolean 3-satisfiability problem to a planar incidence graph.
In an undirected graph, reachability between all pairs of vertices can be determined by identifying the connected components of the graph. Any pair of vertices in such a graph can reach each other if and only if they belong to the same connected component; therefore, in such a graph, reachability is symmetric (reaches iff reaches ). The ...
Differential equations or difference equations on such graphs can be employed to leverage the graph's structure for tasks such as image segmentation (where the vertices represent pixels and the weighted edges encode pixel similarity based on comparisons of Moore neighborhoods or larger windows), data clustering, data classification, or ...
If a vertex has degree 7 and has positive final charge, then received charge from at least 6 adjacent degree 5 vertices. Since the graph is a triangulation, the vertices adjacent to must form a cycle, and since it has only degree 7, the degree 5 neighbors cannot be all separated by vertices of higher degree; at least two of the degree 5 ...