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 ...

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 ...

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) = ...

Abstract.For two vertices 𝑢 and 𝑣 of a graph 𝐺, the set 𝐼[𝑢, 𝑣] consists of all vertices lying on some 𝑢 - 𝑣 geodesic in 𝐺. If 𝑆 is a set of vertices of 𝐺, then 𝐼[𝑆] is the union of all ...

Abstract: As a basis of dealing with various constraints arising in IC layout problems we present efficient algorithms for planar embedding of graphs with constraints on vertices in placing them on ...