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An n-component of a graph G is a maximal n-connected subgraph.

A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...

A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not ...

A graph for which the relations between pairs of vertices are symmetric, so that each edge has no directional character (as opposed to a directed graph). Unless otherwise ...

A section of a graph obtained by finding its intersection with a plane.

The double graph of a given graph G is constructed by making two copies of G (including the initial edge set of each) and adding edges u_1v_2 and v_1u_2 for every edge uv of ...

The Franklin graph is the 12-vertex cubic graph shown above whose embedding on the Klein bottle divides it into regions having a minimal coloring using six colors, thus ...

An apex graph is a graph possessing at least one vertex whose removal results in a planar graph. The set of vertices whose removal results in a planar graph is known as the ...

A three-colorable graph G is a graph with chromatic number chi(G)<=3.

The Kittell graph is a planar graph on 23 nodes and 63 edges that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof of ...