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NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2 Feedback vertex set [2] [3]: GT7 Feedback arc set [2] [3]: GT8 Graph coloring [2] [3]: GT4
The minimum vertex cover problem is the optimization problem of finding a smallest vertex cover in a given graph. INSTANCE: Graph G {\displaystyle G} OUTPUT: Smallest number k {\displaystyle k} such that G {\displaystyle G} has a vertex cover of size k {\displaystyle k} .
Another problem in subdivision containment is the Kelmans–Seymour conjecture: Every 5-vertex-connected graph that is not planar contains a subdivision of the 5-vertex complete graph K 5. Another class of problems has to do with the extent to which various species and generalizations of graphs are determined by their point-deleted subgraphs ...
A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. [1] [2] [3]
A classical example is the problem of enumeration of the vertices of a convex polytope specified by a set of linear inequalities: [1] A x ≤ b {\displaystyle Ax\leq b} where A is an m × n matrix, x is an n ×1 column vector of variables, and b is an m ×1 column vector of constants.
In mathematics, an extreme point of a convex set in a real or complex vector space is a point in that does not lie in any open line segment joining two points of . In linear programming problems, an extreme point is also called vertex or corner point of S . {\displaystyle S.} [ 1 ]
Famous examples are claw-free graphs, [11] P 5-free graphs [12] and perfect graphs. [13] For chordal graphs, a maximum weight independent set can be found in linear time. [14] Modular decomposition is a good tool for solving the maximum weight independent set problem; the linear time algorithm on cographs is the basic example for
Formally, an edge cover of a graph G is a set of edges C such that each vertex in G is incident with at least one edge in C.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).