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A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

The pentatope graph is the skeleton of the pentatope, namely the complete graph K_5. It is sometimes also known as the Kuratowski graph (Nikolić et al. 2000, p. 281). Since ...

A graph is a forbidden (vertex-)induced subgraph if its presence as a vertex-induced subgraph of a given graph means it is not a member of some family of graphs. For example, ...

A graph embedding, sometimes also called a graph drawing, is a particular drawing of a graph. Graph embeddings are most commonly drawn in the plane, but may also be ...

An automorphic graph is a distance-transitive graph Gamma for which the automorphism group Aut(Gamma) acts primitively on the vertices of Gamma and is not a complete graph or ...

The edge connectivity, also called the line connectivity, of a graph is the minimum number of edges lambda(G) whose deletion from a graph G disconnects G. In other words, it ...

An edge-magic graph is a labeled graph with e graph edges labeled with distinct elements {1,2,...,e} so that the sum of the graph edge labels at each graph vertex is the ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...