Graph families | Hypergraphs | Graph theory | Graph minor theory

Forbidden graph characterization

In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to the family and further exclude all graphs from the family which contain any of these forbidden graphs as (induced) subgraph or minor. A prototypical example of this phenomenon is Kuratowski's theorem, which states that a graph is planar (can be drawn without crossings in the plane) if and only if it does not contain either of two forbidden graphs, the complete graph K5 and the complete bipartite graph K3,3. For Kuratowski's theorem, the notion of containment is that of graph homeomorphism, in which a subdivision of one graph appears as a subgraph of the other. Thus, every graph either has a planar drawing (in which case it belongs to the family of planar graphs) or it has a subdivision of at least one of these two graphs as a subgraph (in which case it does not belong to the planar graphs). (Wikipedia).

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Isolated Vertex - Graph Theory

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From playlist Graph Theory

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What is a graph? A graph theory graph, in particular, is the subject of discussion today. In graph theory, a graph is an ordered pair consisting of a vertex set, then an edge set. Graphs are often represented as diagrams, with dots representing vertices, and lines representing edges. Each

From playlist Graph Theory

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From playlist Graph Theory

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From playlist Graph Theory

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From playlist Graph Theory part-1

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From playlist Combinatorics

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From playlist Introduction to Algorithms

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From playlist Mathematics

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From playlist Mathematics

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From playlist Graph Theory part-1

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From playlist Combinatorics

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From playlist Graph Theory

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From playlist Graph Theory

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From playlist Global Noncommutative Geometry Seminar (Europe)

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From playlist Combinatorics

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From playlist Data structures

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Using networks to detect dynamical regime change in time series by Michael Small

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