That result allowed them to prove that on an n-node graph, order nlog(log(n)) edges will surely contain a regular graph with degree 3 or more.The order of the solution is the same whether you’re ...

The One Factorization Conjecture: Let G be a k-regular graph of even order n, where k is at least n/2. Then G is 1-factorable. Chetwynd and Hilton [1] proved the conjecture under a stronger assumption ...

A k-regular graph shows the minimal number of links required by a k-connected graph, leading tominimal flooding cost. The paper formally shows, in particular, that there are an infinite number of ...

We consider networks formed by the union of M random 1-regular directed graphs. These graphs are also called permutation models in the literature. We first present a proof showing that the expansion ...

This post offers reasons for using logarithmic scales, also called log scales, on charts and graphs. It explains when logarithmic graphs with base 2 are preferred to logarithmic graphs with base 10.