Let G = (V,E) be a graph and let v ∈ V. Let IRS(v,G) denote the maximum cardinality of an irredundant set in G which contains v. Then IRS(G) = min {IRS(v,G) : v ∈ V } is called the irredundance saturation number of G. In this paper we initiate a study of this parameter.

Given graphs G and H, G is H-saturated if H is not a subgraph of G, but for all e / ∈ E(G), H appears as a subgraph of G + e. While for every n > |V (H)|, there exists an n-vertex graph that is H-saturated, the same does not hold for induced subgraphs. That is, there exist graphs H and values of n > |V (H)|, for which every n-vertex graph G either contains H as an induced subgraph, or there exi...

Abstract. Consider Dyson’s Hermitian Brownian motion model after a finite time S, where the process is started at N equidistant points on the real line. These N points after time S form a determinantal process and has a limit as N → ∞. This limting determinantal proceess has the interesting feature that it shows number variance saturation. The variance of the number of particles in an interval ...

Given a family F and a host graph H, a graph G ⊆ H is F-saturated relative to H if no subgraph of G lies in F but adding any edge from E(H)−E(G) to G creates such a subgraph. In the F-saturation game on H, players Max and Min alternately add edges of H to G, avoiding subgraphs in F , until G becomes F-saturated relative to H. They aim to maximize or minimize the length of the game, respectively...

residual gas saturation is one of the most important parameter in determining recovery factor of water-drive gas reservoir. visual observation of processes occurring at the pore level in micromodels can give an insight to fluid displacements at the larger scale and also help the interpretation of production performance at reservoir scale. in this study experimental tests in a glass micromodel w...