Given a family of (hyper)graphs $\mathcal{F}$ a (hyper)graph $G$ is said to be $\mathcal{F}$-saturated if $G$ is $F$-free for any $F \in\mathcal{F}$ but for any edge e in the complement of $G$ the… Expand

Given a family of graphs F , a graph G is F-saturated if no element of F is a subgraph of G, but for any edge e in G, some element of F is a subgraph of G + e. Let sat(n,F) denote the minimum number… Expand

A graph $G$ is said to be F -saturated if G contains no copy of F as a subgraph, but for any edge in the complement of $G$, the graph does contain a cycle of length $l$.Expand

We give an upper bound for sat(n,F) when F=K"t^2 the complete t-partite graph with partite sets of size 2, and prove equality when G is of prescribed minimum degree.Expand

A 1993 result of Alon and Füredi gives a sharp upper bound on the number of zeros of a multivariate polynomial over an integral domain in a finite grid, assuming a certain ‘Condition (D)’ on the grid which holds vacuously when the ring is a domain.Expand

Tumorigenesis can be induced either by activating cell proliferation or by inhibiting metabolic pathways regulating programmed cell death (apoptosis). There is evidence suggesting that p60(v-src) and… Expand

For any simple graph H, let σ(H,n) be the minimum m so that for any realizable degree sequence π = (d1, d2, . . . , dn) with sum of degrees at least m, there exists an n-vertex graph G witnessing π that contains H as a weak subgraph.Expand