Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
On the SPANNING k-TREE problem
Discrete Applied Mathematics
On spanning 2-trees in a graph
Discrete Applied Mathematics
Graph classes: a survey
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Intersection graph algorithms
Network design problems: steiner trees and spanning k -trees
Network design problems: steiner trees and spanning k -trees
Graph Theory With Applications
Graph Theory With Applications
Hi-index | 0.00 |
A locally connected spanning tree T of a graph G is a spanning tree of G with the following property: for every vertex, its neighbourhood in T induces a connected subgraph in G. The existence of such a spanning tree in a network ensures, in case of site and line failures, effective communication amongst operative sites as long as these failures are isolated.We prove that the problem of determining whether a graph contains a locally connected spanning tree is NP-complete, even when input graphs are restricted to planar graphs or split graphs. On the other hand, we obtain a linear-time algorithm for finding a locally connected spanning tree in a directed path graph, and a linear-time algorithm for adding fewest edges to a graph to make a given spanning tree of the graph a locally connected spanning tree of the augmented graph.