We prove that any graph G with n points has a distribution T over spanning trees such that for any edge (u, v) the expected stretch ET ∼T [dT (u, v)/dG(u, v)] is bounded by ˜O(...
The Fibonacci number of a graph is the number of independent vertex subsets. In this paper, we investigate trees with large Fibonacci number. In particular, we show that all trees...
Arnold Knopfmacher, Robert F. Tichy, Stephan Wagne...
For z1, z2, z3 Zn, the tristance d3(z1, z2, z3) is a generalization of the L1-distance on Zn to a quantity that reflects the relative dispersion of three points rather than two. ...
A Shilla distance-regular graph (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divide...
Inspired by the recent interest in combining geometry with random graph models, we explore in this paper two generalizations of the random dot product graph model proposed by Kraet...