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1 Examples and types of graphs. 2 Graph coloring. 3 Paths and cycles. ... Download as PDF; Printable version; ... Museum guard problem; Wheel graph; Graph coloring
Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms ...
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...
Resolving sets for graphs were introduced independently by Slater (1975) and Harary & Melter (1976), while the concept of a resolving set and that of metric dimension were defined much earlier in the more general context of metric spaces by Blumenthal in his monograph Theory and Applications of Distance Geometry. Graphs are special examples of ...
The complete list of all free trees on 2, 3, and 4 labeled vertices: = tree with 2 vertices, = trees with 3 vertices, and = trees with 4 vertices.. In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the ...
The vertex set of an n-vertex graph may be identified with the integers from 1 to n, and using such an identification a canonical form of a graph may also be described as a permutation of its vertices. Canonical forms of a graph are also called canonical labelings, [4] and graph canonization is also sometimes known as graph canonicalization.
An example of how intersecting sets define a graph. In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets.Any graph can be represented as an intersection graph, but some important special classes of graphs can be defined by the types of sets that are used to form an intersection representation of them.
The monochromatic triangle problem takes as input an n-node undirected graph G(V,E) with node set V and edge set E. The output is a Boolean value, true if the edge set E of G can be partitioned into two disjoint sets E1 and E2, such that both of the two subgraphs G1(V,E1) and G2(V,E2) are triangle-free graphs, and false otherwise.