Just as ice crystals form when the temperature dips below zero degrees Celsius, the emergence of a particular property suddenly becomes extremely likely as more edges get added to the graph. When ...

In 1984, the mathematician Józef Dodziuk showed that all these measures of expansion are linked through one quantity — at least, for certain types of graphs. On these so-called regular graphs, every ...

For 65 years, Rand Corp.’s reference book “A Million Random Digits with 100,000 Normal Deviates” has enjoyed a reputation as the go-to source for random numbers. Until, on a random whim ...

Szemerédi’s Regularity Lemma: A partitioning result that decomposes large graphs into a bounded number of random-like subgraphs. Graph Limit Theory and Random Structures Publication Trend.