In this paper we study collective additive tree spanners for families of graphs that either contain or are contained in AT-free graphs. We say that a graph G = (V, E) admits a sys...
It has long been known that the number of spanning trees in circulant graphs with fixed jumps and n nodes satisfies a recurrence relation in n. The proof of this fact was algebra...
Abstract. The node-weighted Steiner tree problem is a variation of classical Steiner minimum tree problem. Given a graph G = (V, E) with node weight function C : V → R+ and a sub...
Xianyue Li, Xiao-Hua Xu, Feng Zou, Hongwei Du, Pen...
Given a graph G and a spanning tree T of G, we say that T is a tree t-spanner of G if the distance between every pair of vertices in T is at most t times their distance in G. The p...
We study the empire colouring problem (as defined by Percy Heawood in 1890) for maps whose dual planar graph is a tree, with empires formed by exactly r countries. We prove that, ...