It is commonly believed that vertex-transitive graphs (and in particular Cayley graphs) tend to contain hamilton cycles. The only known connected vertex-transitive graphs without hamilton cycles are K ...

We consider a random object that is associated with both random walks and random media, specifically, the superposition of a configuration of subcritical Bernoulli percolation on an infinite connected ...

Combinatorics and discrete mathematics form a vibrant and expansive branch of modern mathematics, dedicated to the study of finite or countable structures and the methods used to count, classify, and ...

In 2008, the mathematician Oded Schramm died in a hiking accident in the Cascade mountains some 50 miles east of Seattle. Though he was just 46 years old, he had constructed entirely new areas of ...