Planar graph and Three utilities problem

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Difference between Planar graph and Three utilities problem

Planar graph vs. Three utilities problem

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. The classical mathematical puzzle known as the three utilities problem; the three cottages problem or sometimes water, gas and electricity can be stated as follows: The problem is an abstract mathematical puzzle which imposes constraints that would not exist in a practical engineering situation.

Complete bipartite graph

No description.

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Complete graph

No description.

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Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

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Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

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Graph embedding

In topological graph theory, an embedding (also spelled imbedding) of a graph G on a surface \Sigma is a representation of G on \Sigma in which points of \Sigma are associated with vertices and simple arcs (homeomorphic images of) are associated with edges in such a way that.

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Graph minor

In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges and vertices and by contracting edges.

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Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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K-vertex-connected graph

In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed.

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Kazimierz Kuratowski

Kazimierz Kuratowski (Polish pronunciation:, 2 February 1896 – 18 June 1980) was a Polish mathematician and logician.

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Kuratowski's theorem

In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski.

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Toroidal graph

In mathematics, a toroidal graph is a graph that can be embedded on a torus.

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Torus

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

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Wagner's theorem

In graph theory, Wagner's theorem is a mathematical forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite graph is planar if and only if its minors include neither K5 (the complete graph on five vertices) nor K3,3 (the utility graph, a complete bipartite graph on six vertices).

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