Department of Mathematics, Velammal Engineering College, Chennai, India. We begin with the plane coloring problem. What is the least number of colors needed to color all the points of the Euclidean ...

Let the number of vertices in a graph be $n$. We have to compute the number $G_n$ of labeled graphs with $n$ vertices (labeled means that the vertices are marked with ...

Carpathian Journal of Mathematics, Vol. 39, No. 2 (2023), pp. 371-382 (12 pages) The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. In ...

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 ...

1 Department of Mathematics, Bengaluru City University, Central College Campus, Bengaluru, India. 2 Department of Mathematics, Bangalore University, Bengaluru, India. Products of structures are a ...

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) = ...

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 ...

Abstract: To determine a minimum set of arcs of an arbitrary directed graph which, if removed, leave the graph without directed circuits, is an outstanding problem in graph theory. A related problem ...

Abstract: The second smallest eigenvalue of the Laplacian matrix, also known as the algebraic connectivity, characterizes the performance of some dynamic processes on networks, such as consensus in ...

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 ...