β Scribed by William Mitchell
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A subset of vertices is a maximum independent set if no two of the vertices are joined by an edge and the subset has maximum cardinality. In this paper we answer a question posed by Herb Wilf. We show that the greatest number of maximum independent sets for a tree of n vertices is 2(n-3\* for odd n
## Abstract Let __G__ be a graph and __f__ be a mapping from __V__(__G__) to the positive integers. A subgraph __T__ of __G__ is called an __f__βtree if __T__ forms a tree and __d__~__T__~(__x__)β€__f__(__x__) for any __x__β__V__(__T__). We propose a conjecture on the existence of a spanning __f__βt
By using the notion of compatibility of subgraphs with a perfect matching developed for digraphs in [1], we show that if, in a balanced bipartite graph G of minimum degree 6, the maximum cardinality ebip of a balanced independent subset satisfies ~bip ~< 26 --4, then G is hamiltonian-biconnected, an
## Abstract The number of independent vertex subsets is a graph parameter that is, apart from its purely mathematical importance, of interest in mathematical chemistry. In particular, the problem of maximizing or minimizing the number of independent vertex subsets within a given class of graphs has