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An extremal graph in which the forced triangles are all the same color. Call R the number of red monochromatic forced triangles and B the number of blue monochromatic forced ...

The study of how the intrinsic structure of graphs ensures certain types of properties (e.g., clique-formation and graph colorings) under appropriate conditions.

A graph G with m edges is said to be elegant if the vertices of G can be labeled with distinct integers (0,1,2,...,m) in such a way that the set of values on the edges ...

Given a "good" graph G (i.e., one for which all intersecting graph edges intersect in a single point and arise from four distinct graph vertices), the crossing number is the ...

A lobster graph, lobster tree, or simply "lobster," is a tree having the property that the removal of leaf nodes leaves a caterpillar graph (Gallian 2007). The numbers of ...

There exists no known P algorithm for graph isomorphism testing, although the problem has also not been shown to be NP-complete. In fact, the problem of identifying ...

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 graph G is fully reconstructible in C^d if the graph is determined from its d-dimensional measurement variety. If G is globally rigid in R^d on n>=d+2 vertices, then G is ...

A weakly perfect graph is a graph for which omega(G)=chi(G) (without any requirement that this condition also hold on induced subgraphs, which is required for a graph to be ...

A directed strongly regular graph is a simple directed graph with adjacency matrix A such that the span of A, the identity matrix I, and the unit matrix J is closed under ...