Updating the Hamiltonian problem—a survey
Journal of Graph Theory
Finding long paths and cycles in sparse Hamiltonian graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A matter of degree: improved approximation algorithms for degree-bounded minimum spanning trees
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Multiwavelength Optical Networks: A Layered Approach
Multiwavelength Optical Networks: A Layered Approach
Low-Degree Spanning Trees of Small Weight
SIAM Journal on Computing
Spanning Trees with Bounded Number of Branch Vertices
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Graphs and Hypergraphs
Hi-index | 0.00 |
A spanning spider for a graph G is a spanning tree T of G with at most one vertex having degree three or more in T. In this paper we give density criteria for the existence of spanning spiders in graphs. We constructively prove the following result: Given a graph G with n vertices, if the degree sum of any independent triple of vertices is at least n - 1, then there exists a spanning spider in G. We also study the case of bipartite graphs and give density conditions for the existence of a spanning spider in a bipartite graph. All our proofs are constructive and imply the existence of polynomial time algorithms to construct the spanning spiders. The interest in the existence of spanning spiders originally arises in the realm of multicasting in optical networks. However, the graph theoretical problems discussed here are interesting in their own right.