A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections. “It’s a bit of a surprise, at least for me, that such a combination ...

Geometric intersection graphs form an intriguing class of structures in which vertices represent geometric objects – such as line segments, discs, or curves – and an edge is established between two ...

It has been an exhilarating year in combinatorics research. In early 2023, mathematicians were stunned when two of the biggest problems in the field were solved in as many months. Now, a third major ...

This is a preview. Log in through your library . Abstract Let HG(x, y) be the expected hitting time from vertex x to vertex y for the first time on a simple connected graph G and φ(G) = ...

A map f : V → {0, 1, 2} is a Roman dominating function on a graph G = (V, E) if for every vertex v ∈ V with f(v) = 0, there exists a vertex u, adjacent to v, such that f(u) = 2. The weight of a Roman ...