β Scribed by Peter J. Slater
No coin nor oath required. For personal study only.
Consider a collection of disjoint paths in graph G such that every vertex is on one of these paths. The size of the smallest such collection is denoted i(G). A procedure for forming such collections is established. Restricting attention to trees, the range of values for the sizes of the collections obtained is examined, and a constructive characterization of trees If for which one always obtains a collection of size i(T) is presented.
π SIMILAR VOLUMES
This article describes methods for finding an optimal location for a path-shaped or tree-shaped facility of a specified size in a tree network. Four optimization criteria are examined: minimizing distancesum, minimizing eccentricity, maximizing distancesum, and maximizing eccentricity.
In this article we begin the study of the vertex subsets of a graph G which consist of the vertices contained in all, or in no, respectively, minimum dominating sets of G. We characterize these sets for trees, and also obtain results on the vertices contained in all minimum independent dominating se
The following problem is investigated. Given an undirected graph G, determine the smallest cardinality of a vertex set that meets all complete subgraphs KC G maximal under inclusion.