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A Survey of Minimum Saturated Graphs
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 $G$ theExpand
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Saturation numbers for families of Ramsey-minimal graphs
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 numberExpand
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On the size and structure of graphs with a constant number of 1-factors
TLDR
We investigate the maximum number of edges in a graph with a prescribed number of 1-factors and examine the structure of such extremal graphs. Expand
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Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size
TLDR
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
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A note on minimum K2, 3-saturated graphs
TLDR
We determine the asymptotic behavior for the minimum number of edges in a K2,3-saturated graph of given order n. Expand
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Minimum degree and the minimum size of K22-saturated graphs
TLDR
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
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On Zeros of a Polynomial in a Finite Grid
TLDR
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
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Potentially H-bigraphic sequences
TLDR
We extend the notion of a potentially H-graphic sequence as follows. Expand
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The product of the v-src-inducible gene nr-13 is a potent anti-apoptotic factor.
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) andExpand
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Graphic Sequences with a Realization Containing a Friendship Graph
TLDR
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
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