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The Heawood four-color graph is the 25-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's ...

The Hochberg-O'Donnell fish graph is the unit-distance graph on 23 nodes and 42 edges illustrated above. It is triangle-free and is the smallest example of a unit-distance ...

A hypergraph is a graph in which generalized edges (called hyperedges) may connect more than two nodes.

The concept of irredundance was introduced by Cockayne et al. (1978). Let N_G[v] denote the graph neighborhood of a vertex v in a graph G (including v itself), and let N_G[S] ...

The kite graph is the 5-vertex graph illustrated above (Brandstädt et al. 1987, p. 18). It is implemented in the Wolfram Language as GraphData["KiteGraph"]. Unfortunately, ...

The Kuratowski reduction theorem states that very nonplanar graph contains either the utility graph UG=K_(3,3) or the pentatope graph K_5 as a graph minor. The graphs K_(3,3) ...

Let (P,B) denote a configuration with v points P={p_1,...,p_v} and b lines ("blocks") B=(B_1,...,B_b). Then the Levi graph L(P,B), also called the incidence graph, of a ...

A graph G is said to be locally X, where X is a graph (or class of graphs), when for every vertex v, the graph induced on G by the set of adjacent vertices of V (sometimes ...

An odd chordless cycle is a chordless cycle of length >4. A graph is said to be perfect iff neither the graph G nor its graph complement G^_ has an odd chordless cycle. A ...

An ordered pair representation is a representation of a directed graph in which edges are specified as ordered pairs or vertex indices. The ordered pairs representation of a ...