Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory. This past October, as Jacob Holm and Eva Rotenberg were thumbing through a ...

In algorithms, as in life, negativity can be a drag. Consider the problem of finding the shortest path between two points on a graph — a network of nodes connected by links, or edges. Often, these ...

When you get stuck on a fiendishly difficult sudoku, it’s hard not to wonder if the puzzle really has a solution. At another moment, aglow in the triumph of a clever deduction, you might have a ...

On independent random points U1,⋯ ,Un distributed uniformly on [0,1]d, a random graph Gn(x) is constructed in which two distinct such points are joined by an edge ...

The manner in which patches are delineated in spatially realistic metapopulation models will influence the size, connectivity, and extinction and recolonization dynamics of those patches. Most ...

Researchers thought that they were five years away from solving a math riddle from the 1980's. In reality, and without knowing, they had nearly cracked the problem and had just given away much of the ...