We show that a graph of girth greater than 6 log k + 3 and minimum degree at least 3 has a minor of minimum degree greater than k. This is best possible up to a factor of at most 9/4. As a corollary, every graph of girth at least 6 log r + 3 log log r + c and minimum degree at least 3 has a Kr minor.

The sequence of frond emergence and the intervals required for daughter colony separation have been determined for Lemna paucicostata Hegelm. 6746 growing under standardized conditions. After separation of a new mother colony, the first daughter colony is produced from the left meristematic pocket and separates after approximately 60 hours, the second daughter, produced from the right pocket, s...

The Gram dimension gd(G) of a graph is the smallest integer k ≥ 1 such that, for every assignment of unit vectors to the nodes of the graph, there exists another assignment of unit vectors lying in R, having the same inner products on the edges of the graph. The class of graphs satisfying gd(G) ≤ k is minor closed for fixed k, so it can characterized by a finite list of forbidden minors. For k ...