A set P of disjoint paths in a graph G is called a (complete) path cover of G if every vertex of G belongs to one of the paths in P. A path cover of any subgraph of G is called a partial path cover of G. For xed k > 0, a k-blanket of graph G is a partial path cover P of G, consisting of exactly k paths, that maximizes the size of the subgraph covered by P. A k-core of graph G is a partial path ...

understanding the relationship between root yield and other traits in sugar beet may be a crucial step towards successful breeding of this important crop. path analysis provides a useful method in analyzing the genetic and phenotypic coefficients of correlations. this method is able to effectively unveil direct and indirect effects among traits of interest. in this research, root yield, yield c...

In the double TSP with multiple stacks, a vehicle with several stacks performs a Hamiltonian circuit to pick up some items and stores them in its stacks. It then delivers every item by performing another Hamiltonian circuit while satisfying the last-in-first-out policy of its stacks. The consistency requirement ensuring that the pickup and delivery circuits can be performed by the vehicle is th...

In this paper, we study a variant of the path cover problem, namely, the terminal path cover problem. Given a graph G and a subset T of vertices of G, a terminal path cover of G with respect to T is a set of pairwise vertex-disjoint paths PC that covers the vertices of G such that the vertices of T are all endpoints of the paths in PC. The terminal path cover problem is to find a terminal path ...

This improves an earlier result of the first author for k = n = 2, namely Theorem II below, which dealt with B2 -sequences. This notion arose from a paper of Sidon [6]. A strictly increasing sequence A of natural numbers a,, a2 . . . . is called a B2-sequence, if for any two pairs (i, j) + (k, m) of natural numbers i <j, k < m there holds aj a i + ak a„„ in short, if A has no double-differences...

We consider log-convex sequences that satisfy an additional constraint imposed on their rate of growth. We call such sequences log-balanced. It is shown that all such sequences satisfy a pair of double inequalities. Sufficient conditions for log-balancedness are given for the case when the sequence satisfies a two(or more-) term linear recurrence. It is shown that many combinatorially interesti...

In a closed 2-cell embedding of a graph each face is homeomorphic to an open disk and is bounded by a cycle in the graph. The Orientable Strong Embedding Conjecture says that every 2-connected graph has a closed 2-cell embedding in some orientable surface. This implies both the Cycle Double Cover Conjecture and the Strong Embedding Conjecture. In this paper we prove that every 2-connected proje...

We consider a model for diffusive phase transitions, for instance, the component separation in a binary mixture. Our model is described by two functions, the absolutete temperature θ := θ(t, x) and the order parameter w := w(t, x), which are governed by a system of two nonlinear parabolic PDEs. The order parameter w is constrained to have double obstacles σ∗ ≤ w ≤ σ∗ (i.e., σ∗ and σ∗ are the th...

We discuss N = 2 SU(2) Yang-Mills gauge theories coupled with Nf (= 2, 3) massive hypermultiplets in the weak coupling limit. We determine the exact massive prepotentials and the monodromy matrices around the weak coupling limit. We also study that the double scaling limit of these massive theories and find that the massive Nf − 1 theory can be obtained from the massive Nf theory. New formulae ...

A directed cycle double cover of a graph G is a family of cycles of G, each provided with an orientation, such that every edge of G is covered by exactly two oppositely directed cycles. Explicit obstructions to the existence of a directed cycle double cover in a graph are bridges. Jaeger [4] conjectured that bridges are actually the only obstructions. One of the difficulties in proving the Jaeg...