The definitions of these matroids, with a summary of their interesting properties, can be found in the Appendix. Except for P"8 , they were all known to be excluded minors for GF(4)-representability (see Oxley [15, 17]). The matroid P"8 is obtained by relaxing the unique pair of disjoint circuit-hyperplanes of P8 . Ever since Whitney's introductory paper [28] on matroid theory, researchers have...

We prove upper and lower bounds on the size of the largest square grid graph that is a subgraph, minor, or shallow minor of a graph in the form of a larger square grid from which a specified number of vertices have been deleted. Our bounds are tight to within constant factors. We also provide less-tight bounds on analogous problems for higher-dimensional grids.

A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class G, let gn be the number of graphs in G which have n vertices. The growth constant of G is γ = lim sup(gn/n!) . We study the properties of the set Γ of growth constants of minor-closed classes of graphs. Among other results, we show that Γ does not contai...

-In the flavonol biosynthetic pathway of Petunia 'Mitchell', polyploidy has a differential effect increasing the relative concentration of the major metabolite quercetin-3-sophoroside and decreasing the relative concentration of the minor metabolite quercetin-3,7-diglucoside. It has no effect on the total concentration or on the concentration of the other four minor flavonols.

some studies suggested that glucocorticoid receptors activities can modulate fear and anxiety. according to that, the purpose of this research is to assess the modulatory effect of glucocorticoid receptors on the anxiety assessed in plus maze. in this research mice with medium weight of 20-25 g were used. the male and female animals separately sorted in two groups as control and experiment rand...