A k?coloring of an oriented graph G = (V; A) is an assignment c of one of the colors 1; 2; : : :; k to each vertex of the graph such that, for every arc (x; y) of G, c(x) 6 = c(y). The k?coloring is good if for every arc (x; y) of G there is no arc (z; t) 2 A such that c(x) = c(t) and c(y) = c(z). A k?coloring is said to be semi?strong if for every vertex x of G, c(z) 6 = c(t) for any pair fz; ...

Given a graph G = (V; E) and two vertices s; t 2 V , s 6 = t, the Menger problem is to nd a maximum number of disjoint paths connecting s and t. Depending on whether the input graph is directed or not, and what kind of disjointness criterion is demanded, this general formulation is specialized to the directed or undirected vertex, and the edge or arc disjoint Menger problem, respectively. For p...

Given a graph G V E and two vertices s t V s t the Menger problem is to nd a maximum number of disjoint paths connecting s and t Depending on whether the input graph is directed or not and what kind of disjointness criterion is demanded this general formulation is specialized to the directed or undirected vertex and the edge or arc disjoint Menger problem respectively For planar graphs the edge...

Given a graph G = (V, E) and two vertices s, t ∈ V , s 6= t , the Menger problem is to find a maximum number of disjoint paths connecting s and t . Depending on whether the input graph is directed or not, and what kind of disjointness criterion is demanded, this general formulation is specialized to the directed or undirected vertex, and the edge or arc disjoint Menger problem, respectively. Fo...

A tournament T = (V,A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs whose removal results in an acyclic digraph. The Feedback Arc Set problem restricted to tournaments is known as the k-Feedback Arc Set in Tou...

4 We consider the problem of deciding whether a given network with integer capacities has two 5 feasible flows x and y with prescribed balance vectors such that the arcs that carry flow in x are 6 arc-disjoint from the arcs that carry flow in y. This generalizes a number of well-studied problems 7 such as the existence of arc-disjoint out-branchings B s , B + t where the roots s, t may be the s...

In this paper we study k-noncrossing RNA structures with minimum arc-length 4 and at most k − 1 mutually crossing bonds. Let T k (n) denote the number of knoncrossing RNA structures with arc-length ≥ 4 over n vertices. We prove (a) a functional equation for the generating function ∑ n≥0 T [4] k (n)z n and (b) derive for k ≤ 9 the asymptotic formula T k (n) ∼ ck n +(k−1)/2) γ k . Furthermore we ...

In this paper we study k-noncrossing RNA structures with minimum arc-length 4 and at most k − 1 mutually crossing bonds. Let T [4] k (n) denote the number of k-noncrossing RNA structures with arc-length ≥ 4 over n vertices. We prove (a) a functional equation for the generating function P n≥0 T [4] k (n)z n and (b) derive for k ≤ 9 the asymptotic formula T [4] k (n) ∼ c k n −((k−1) 2 +(k−1)/2) γ...

Introduction: Cardiac cine MRI (CMRI) is a routine exam for studying myocardium functionality. High spatiotemporal-resolution CMRI has been challenging, limited by breathhold capability. Recently, various k-t techniques [1,2] have been developed to achieve acceleration factors (AF) ≥3 in dynamic imaging by incorporating temporal correlations. Among these approaches, k-t GRAPPA possesses the adv...

The dorsal striatum is involved in motor-response learning, but the extent to which distinct populations of striatal efferent neurons are differentially involved in such learning is unknown. Activity-regulated, cytoskeleton-associated (Arc) protein is an effector immediate-early gene implicated in synaptic plasticity. We examined arc mRNA expression in striatopallidal vs. striatonigral efferent...