An elegant and general way to apply graph partitioning algorithms to hypergraphs would be to model hypergraphs by graphs and apply the graph algorithms to these models Of course such models have to simulate the given hypergraphs with respect to their cut properties An edge weighted graph V E is a cut model for an edge weighted hypergraph V H if the weight of the edges cut by any bipartition of ...

We study the maximum flow problem in an undirected planar network with both edge and vertex capacities (EVC-network). A previous study reduces the minimum cut problem in an undirected planar EVC-network to the minimum edge-cut problem in another planar network with edge capacity only (EC-network), thus the minimum-cut or the maximum flow value can be computed in O(n log n) time. Based on this r...

Let C be a uniform clutter and let I = I(C) be its edge ideal. We prove that if C satisfies the packing property (resp. max-flow min-cut property), then there is a uniform Cohen-Macaulay clutter C1 satisfying the packing property (resp. max-flow min-cut property) such that C is a minor of C1. For arbitrary edge ideals of clutters we prove that the normality property is closed under parallelizat...

The aim of this study was to determine why food poisoning bacteria attached to cut cabbage are not efficiently disinfected by sodium hypochlorite (NaClO). Pretreatment of shredded cabbage with diethyl ether definitely decreased the survival numbers of Escherichia coli O157:H7 and Salmonella spp. after disinfection with 100 ppm of NaClO. The density of E. coli O157:H7 at the cut edge of a cabbag...

For a connected graphG= (V ,E), an edge set S ⊂ E is a k-restricted-edge-cut, ifG−S is disconnected and every component of G− S has at least k vertices. The k-restricted-edge-connectivity of G, denoted by k(G), is defined as the cardinality of a minimum k-restricted-edge-cut. The k-isoperimetric-edge-connectivity is defined as k(G)=min{|[U,U ]| : U ⊂ V, |U | k, |U | k}, where [U,U ] is the set ...

The computational complexity of multicut-like problems may vary significantly depending on whether the terminals are fixed or not. In this work we present a comprehensive study of this phenomenon in two types of cut problems in directed graphs: double cut and bicut. 1. Fixed-terminal edge-weighted double cut is known to be solvable efficiently. We show that fixed-terminal node-weighted double c...

In this note we report on our recent work, still in progress, regarding Folkman numbers. Let f(2, 3, 4) denote the smallest integer n such that there exists a K4– free graph of order n having that property that any 2–coloring of its edges yields at least one monochromatic triangle. It is well–known that such a number must exist [4,10]. For almost twenty years the best known upper bound, given b...

Graph cut minimization formulates the segmentation problem as the liner combination of data and smoothness terms. The smoothness term is included in the energy formulation through a regularization parameter. We propose that the trade-off between the data and the smoothness terms should not be balanced by the same regularization parameter for the whole image. In order to validate the proposed id...

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

Min-k-cut is the problem of partitioning vertices of a given graph or hypergraph into k subsets such that the total weight of edges or hyperedges crossing different subsets is minimized. For the capacitated min-k-cut problem, each edge has a nonnegative weight, and each subset has a possibly different capacity that imposes an upper bound on its size. The objective is to find a partition that mi...