SettingsComputational problems in graph theory
Canadian traveller problem
In computer science and graph theory, the Canadian Traveller Problem (CTP) is a generalization of the shortest path problem to graphs that are partially observable.
In computer science and graph theory, the Canadian Traveller Problem (CTP) is a generalization of the shortest path problem to graphs that are partially observable.
Clique cover
In computational complexity theory, finding a minimum clique cover is a graph-theoretical NP-complete problem.
In computational complexity theory, finding a minimum clique cover is a graph-theoretical NP-complete problem.
Clique problem
In computer science, the clique problem refers to any of the problems related to finding particular complete subgraphs ("cliques") in a graph, i.e., sets of elements where each pair of elements ...
In computer science, the clique problem refers to any of the problems related to finding particular complete subgraphs ("cliques") in a graph, i.e., sets of elements where each pair of elements ...
Connected dominating set
In graph theory, a connected dominated set and a maximum leaf spanning tree are two closely related structures defined on an undirected graph.
In graph theory, a connected dominated set and a maximum leaf spanning tree are two closely related structures defined on an undirected graph.
Correlation clustering
Correlation clustering operates in a scenario where the relationship between the objects is known instead of the actual representation of the objects.
Correlation clustering operates in a scenario where the relationship between the objects is known instead of the actual representation of the objects.
Degree diameter problem
In graph theory, the degree diameter problem is the problem of finding the largest possible graph G of diameter k such that the largest degree of any of the vertices in G is at most ...
In graph theory, the degree diameter problem is the problem of finding the largest possible graph G of diameter k such that the largest degree of any of the vertices in G is at most ...
Dominating set
In graph theory, a dominating set for a graph G = (V, E) is a subset D of V such that every vertex not in D is joined to at least one member of D by so...
In graph theory, a dominating set for a graph G = (V, E) is a subset D of V such that every vertex not in D is joined to at least one member of D by so...
Edge cover
In graph theory, an edge cover of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set.
In graph theory, an edge cover of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set.
Edge dominating set
In graph theory, an edge dominating set for a graph G = (V, E) is a subset D ⊆ E such that every edge not in D is adjacent to at least one edge i...
In graph theory, an edge dominating set for a graph G = (V, E) is a subset D ⊆ E such that every edge not in D is adjacent to at least one edge i...
Feedback arc set
A feedback arc set (FAS) or feedback edge set is a set of edges which, when removed from the graph, leave a DAG. Put another way, it's a set containing at least one edge of every cy...
A feedback arc set (FAS) or feedback edge set is a set of edges which, when removed from the graph, leave a DAG. Put another way, it's a set containing at least one edge of every cy...
Feedback vertex set
In the mathematical discipline of graph theory, a feedback vertex set of a graph is a set of vertices whose removal leaves a graph without cycles.
In the mathematical discipline of graph theory, a feedback vertex set of a graph is a set of vertices whose removal leaves a graph without cycles.
Graph coloring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
Graph cuts in computer vision
As applied in the field of computer vision, graph cuts can be employed to efficiently solve a wide variety of low-level computer vision problems (early vision), such as image smoothing, the ...
As applied in the field of computer vision, graph cuts can be employed to efficiently solve a wide variety of low-level computer vision problems (early vision), such as image smoothing, the ...
Graph isomorphism problem
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.
Graph partition
In mathematics, the graph partition problem is defined on data represented in the form of a graph G= (V,E), with V vertices and E edges, such that it is possible to partition G...
In mathematics, the graph partition problem is defined on data represented in the form of a graph G= (V,E), with V vertices and E edges, such that it is possible to partition G...
Graph sandwich problem
In graph theory and computer science, the graph sandwich problem is the study of incomplete models of pairwise relations between objects from a certain collection, and how to complete them.
In graph theory and computer science, the graph sandwich problem is the study of incomplete models of pairwise relations between objects from a certain collection, and how to complete them.
Hamiltonian path
In the mathematical field of graph theory, a Hamiltonian path is a path in an undirected graph that visits each vertex exactly once.
In the mathematical field of graph theory, a Hamiltonian path is a path in an undirected graph that visits each vertex exactly once.
Hamiltonian path problem
In the mathematical field of graph theory the Hamiltonian path problem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonian path or a Hamiltonian cycle exist...
In the mathematical field of graph theory the Hamiltonian path problem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonian path or a Hamiltonian cycle exist...
Independent set (graph theory)
In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent.
In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent.
Induced subgraph isomorphism problem
In complexity theory and graph theory, induced subgraph isomorphism is an NP-complete decision problem that involves finding a given graph as an induced subgraph of a larger graph.
In complexity theory and graph theory, induced subgraph isomorphism is an NP-complete decision problem that involves finding a given graph as an induced subgraph of a larger graph.
Instant Insanity
The "Instant Insanity" puzzle consists of four cubes with faces colored with four colors (red, blue, green, and white commonly).
The "Instant Insanity" puzzle consists of four cubes with faces colored with four colors (red, blue, green, and white commonly).
Longest path problem
In the mathematical discipline of graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph.
In the mathematical discipline of graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph.
Longest uncrossed knight's path
The longest uncrossed knight's path is a mathematical problem involving a knight on a standard 8 × 8 chessboard or, more generally, on a square n × n'...
The longest uncrossed knight's path is a mathematical problem involving a knight on a standard 8 × 8 chessboard or, more generally, on a square n × n'...
MaxDDBS
The maximum degree-and-diameter-bounded subgraph problem is a problem in graph theory.
The maximum degree-and-diameter-bounded subgraph problem is a problem in graph theory.
Maximal independent set
In graph theory, a maximal independent set or maximal stable set is an independent set that is not a subset of any other independent set.
In graph theory, a maximal independent set or maximal stable set is an independent set that is not a subset of any other independent set.
Maximum common subgraph isomorphism problem
In complexity theory, maximum common subgraph-isomorphism is an optimization problem that is known to be NP-hard.
In complexity theory, maximum common subgraph-isomorphism is an optimization problem that is known to be NP-hard.
Maximum cut
For a graph, a maximum cut is a cut whose size is not smaller than the size of any other cut.
For a graph, a maximum cut is a cut whose size is not smaller than the size of any other cut.
Metric k-center
In graph theory, the metric k-center, is a combinatorial optimization problem studied in theoretical computer science.
In graph theory, the metric k-center, is a combinatorial optimization problem studied in theoretical computer science.
Minimum k-cut
In mathematics, the minimum k-cut, is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph to k connected components.
In mathematics, the minimum k-cut, is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph to k connected components.
Multi-trials technique
The multi-trials technique by Schneider et al.
The multi-trials technique by Schneider et al.
Pebble motion problems
The pebble motion problems, or pebble motion on graphs, are a set of related problems in graph theory dealing with the movement of multiple objects ('pebbles') from vertex to vertex in a g...
The pebble motion problems, or pebble motion on graphs, are a set of related problems in graph theory dealing with the movement of multiple objects ('pebbles') from vertex to vertex in a g...
Planarity testing
In graph theory, the planarity testing problem asks whether, given a graph, that graph is a planar graph (can be drawn in the plane without edge intersections).
In graph theory, the planarity testing problem asks whether, given a graph, that graph is a planar graph (can be drawn in the plane without edge intersections).
Route inspection problem
In graph theory, a branch of mathematics, the Chinese postman problem, postman tour or route inspection problem is to find a shortest closed path or circuit that visits every edge o...
In graph theory, a branch of mathematics, the Chinese postman problem, postman tour or route inspection problem is to find a shortest closed path or circuit that visits every edge o...
Set TSP problem
In combinatorial optimization, the set TSP, also known as the, group TSP, One-of-a-Set TSP, Multiple Choice TSP or Covering Salesman Problem, is a generalization of the T...
In combinatorial optimization, the set TSP, also known as the, group TSP, One-of-a-Set TSP, Multiple Choice TSP or Covering Salesman Problem, is a generalization of the T...
Shortest path problem
In graph theory, the shortest path problem is the problem of finding a path between two vertices in a graph such that the sum of the weights of its constituent edges is minimized.
In graph theory, the shortest path problem is the problem of finding a path between two vertices in a graph such that the sum of the weights of its constituent edges is minimized.
Snake-in-the-box
The snake-in-the-box problem in graph theory and computer science deals with finding a certain kind of path along the edges of a hypercube.
The snake-in-the-box problem in graph theory and computer science deals with finding a certain kind of path along the edges of a hypercube.
Spanning tree
In the mathematical field of graph theory, a spanning tree T of a connected, undirected graph G is a tree composed of all the vertices and some of the edges of G.
In the mathematical field of graph theory, a spanning tree T of a connected, undirected graph G is a tree composed of all the vertices and some of the edges of G.
Steiner tree problem
The Steiner tree problem, or the minimum Steiner tree problem, named after Jakob Steiner, is a problem in combinatorial optimization, which may be formulated in a number of settings, with ...
The Steiner tree problem, or the minimum Steiner tree problem, named after Jakob Steiner, is a problem in combinatorial optimization, which may be formulated in a number of settings, with ...
Subgraph isomorphism problem
In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a ...
In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a ...
Travelling salesman problem
The travelling salesman problem is an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science.
The travelling salesman problem is an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science.
Unrooted tree path lengths
In computer science, the problem of unrooted tree path lengths is that of finding the number of paths of each length in a tree.
In computer science, the problem of unrooted tree path lengths is that of finding the number of paths of each length in a tree.
Vertex cover
In the mathematical discipline of graph theory, a vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set.
In the mathematical discipline of graph theory, a vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set.
Vertex cycle cover
In mathematics, a vertex cycle cover (commonly called simply cycle cover) of a graph G is a set of cycles which are subgraphs of G and contain all vertices of G.
In mathematics, a vertex cycle cover (commonly called simply cycle cover) of a graph G is a set of cycles which are subgraphs of G and contain all vertices of G.
Widest path problem
In graph algorithms, the widest path problem, also known as the bottleneck shortest path problem or the maximum capacity path problem, is the problem of finding a path between two de...
In graph algorithms, the widest path problem, also known as the bottleneck shortest path problem or the maximum capacity path problem, is the problem of finding a path between two de...