Graph limit theory provides a rigorous framework for analysing sequences of large graphs by representing them as continuous objects known as graphons – symmetric measurable functions on the unit ...

We consider a random walker on a d-regular graph. Starting from a fixed vertex, the first step is a unit step in any one of the d directions, with common probability 1/d for each one. At any later ...

In this paper we consider specific directed graphs called "ladders". The vertices of the graph are randomly colored by green or red. Deleting the edges with at least one red endpoint one gets a random ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

Text: : "Graph Theory" by J. Adrian Bondy and U.S.R. Murty; Graduate Texts in Mathematics 244, Springer 2008. ISBN 978-1-84628-969-9, 2nd printing, 978-1-84628-970-5 (ebook). Notes will be supplied ...

We study the interplay between the diffusion of a harmful state in a network of contacts and the possibility of individual agents to undertake costly investment to protect themselves against infection ...