A simple graph G is k-ordered (respectively, k-ordered hamiltonian) if, for any sequence of k distinct vertices v1, . . . , vk of G, there exists a cycle (respectively, a hamilton...
We present a new bicriteria approximation algorithm for the degree-bounded minimum-cost spanning tree problem: Given an undirected graph with nonnegative edge weights and degree b...
We study the problem of maximizing the broadcast rate in peer-to-peer (P2P) systems under node degree bounds, i.e., the number of neighbors a node can simultaneously connect to is ...
Constructing some regular graph with a given girth, a given degree and the fewest possible vertices is a hard problem. This problem is called the cage graph problem and has some l...
The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-line drawing of G in the plane. We prove that for Δ 5 and all large n, there is a Δ-reg...