The odd edge connectivity of a graph G, denoted by o(G), is the size of a smallest odd edge cut of the graph. Let S be any given surface and be a positive real number. We proved that there is a function fS( ) (depends on the surface S and lim !0 fS( )1⁄41) such that any graph G embedded in S with the odd-edge connectivity at least fS( ) admits a nowhere-zero circular (2þ )-flow. Another major r...

1.1 Max-flow min-cut A flow network is a directed graph D = (V,E) with two distinguished vertices s and t called the source and the sink, respectively. Moreover, each arc (u, v) ∈ E has a certain capacity c(u, v) ≥ 0 assigned to it. Let X be a proper non-empty subset of V . Let X̄ := V −X , then the pair (X, X̄) forms a partition of V , called a cut of D. The set of arcs of D going from X to X̄ is...

a emph{signed graph} (or, in short, emph{sigraph}) $s=(s^u,sigma)$ consists of an underlying graph $s^u :=g=(v,e)$ and a function $sigma:e(s^u)longrightarrow {+,-}$, called the signature of $s$. a emph{marking} of $s$ is a function $mu:v(s)longrightarrow {+,-}$. the emph{canonical marking} of a signed graph $s$, denoted $mu_sigma$, is given as $$mu_sigma(v) := prod_{vwin e(s)}sigma(vw).$$the li...

1. Introduction An efficient algorithm, HALO, is given to compute haloed line drawings of wire frame objects. (Haloed line drawings are described by Appel et al. 1 HALO has two parts: CUT and DRAW. CUT uses an adaptive grid to find all edge intersections. It overlays a square grid, whose fineness is a function of As computer aided design (CAD) deals with more complicated databases, it becomes c...

Graph partitioning has been shown to be an effective way to divide a large computation over an arbitrary number of processors. A good partitioning can ensure load balance and minimize the communication overhead of the computation by partitioning an irregular mesh into p equal parts while minimizing the number of edges cut by the partition. For a large class of irregular mesh applications, the s...

BACKGROUND The present study aimed to evaluate the force delivery of removable thermoplastic appliances (RTAs), modified by different sized incisal cuts, during tipping of a maxillary central incisor in palatal and vestibular direction. METHODS Forty-five RTAs from three different materials (Biolon®, Erkodur®, Ideal Clear®) of the same thickness (1 mm) were used. Analysis was performed on a s...

one of the locations of renal artery atherosclerosis is at the orifice of the renal artery, therefore thestructure of this orifice was assessed in 6 normal, adult male dogs by light microscopy (lm) andtransmission electron microscopy (tem). for the lm study, processed tissues were embedded in paraffinand sectioned serially into 6-μm thickness. sections were stained with orcein. for the tem stud...

PURPOSE To evaluate flap dimensions and cut deterioration with repeated blade use in an automated microkeratome. METHODS The Automated Corneal Shaper (Chiron-Adatomed, Munich, Germany), 160-microm plate attached, was used to make a corneal flap in 90 pig cadaver eyes, reusing blades up to five times. Flap diameter was measured by planimetry and thickness was calculated by ultrasound pachymetr...

We consider the following “multiway cut packing” problem in undirected graphs: given a graph G = (V,E) and k commodities, each corresponding to a set of terminals located at different vertices in the graph, our goal is to produce a collection of cuts {E1, · · · , Ek} such that Ei is a multiway cut for commodity i and the maximum load on any edge is minimized. The load on an edge is defined to b...

Consider the edge-deletion process in which the edges of some finite tree T are removed one after the other in the uniform random order. Roughly speaking, the cut-tree then describes the genealogy of connected components appearing in this edge-deletion process. Our main result shows that after a proper rescaling, the cut-tree of a critical Galton-Watson tree with finite variance and conditioned...