On graphs which contain each tree of given size

On Graphs Which Contain All Sparse Graphs

On graphs which contain all small trees

Communicated by the Managing Editors We investigate those graphs G, with the property that any tree on N vertices occurs as subgraph of G,. In particular, we consider the problem of estimating the minimum number of edges such a graph can have. We show that this number is bounded below and above by $z log II and nl+l/log log %, respectively. A typical question in extremal graph theory1 is one wh...

Generating Functions for Permutations which Contain a Given Descent Set

A large number of generating functions for permutation statistics can be obtained by applying homomorphisms to simple symmetric function identities. In particular, a large number of generating functions involving the number of descents of a permutation σ, des(σ), arise in this way. For any given finite set S of positive integers, we develop a method to produce similar generating functions for t...

Ela on Bipartite Graphs Which Attain Minimum Rank among Bipartite Graphs with a given Diameter

The rank of a graph is defined to be the rank of its adjacency matrix. In this paper, the bipartite graphs that attain the minimum rank among bipartite graphs with a given diameter are completely characterized.

On bipartite graphs which attain minimum rank among bipartite graphs with given diameter

The rank of a graph is defined to be the rank of its adjacency matrix. In this paper, the bipartite graphs that attain the minimum rank among bipartite graphs with a given diameter are completely characterized.