We extend the finite type condition to graph-directed iterated function systems with overlaps. Under this condition, we describe algorithms to compute the box dimension and Hausdorff dimension of the ...

R. Daniel Mauldin, S. C. Williams, Hausdorff Dimension in Graph Directed Constructions, Transactions of the American Mathematical Society, Vol. 309, No. 2 (Oct., 1988 ...

Chayes and Borgs's prior university labors on graph theory and phase transitions have been of some use to the enterprise. Since they joined Microsoft, the World Wide Web has come into its own.

Graph theory, a nearly 300-year-old discipline considered an element of discrete mathematics, is used to model many types of relationships and processes in physical, biological, social and information ...

Engineers could use this breakthrough in graph theory to design wildly efficient quantum computer chips.

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks — vertices (dots) and edges (lines connecting them) — has been an invaluable way ...

Solving sudoku puzzles may not require mathematics, but mathematicians have found plenty to say about the popular brainteasers.

Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a public transportation network. Mathematicians have long sought to develop ...