This paper presents a theorem concerning a matroid with the parity condition. The theorem provides matroid generalizations of graph-theoretic results of Lewin [3] and Gallai [1]. Let M=(E, F) be a matroid, where E is a finite set of elements and F is the family of independent sets of M (in this paper, we presuppose a knowledge of matroid theory; our standard reference is Welsh [4]). Assume that...

A weighted variant of Hall’s condition for the existence of matchings is shown to be equivalent to the existence of a matching in a lexicographic product. This is used to introduce characterizations of those bipartite graphs whose edges may be replicated so as to yield semiregular multigraphs or, equivalently, semiregular edge-weightings. Such bipartite graphs will be called semiregularizable. ...

We perform a matching of the two loop-chiral perturbation theory representation of the scalar Kπ form factor to a dispersive one. Knowing the value of FK/Fπ and f+(0) in the Standard Model (SM) allows to determine two O(p) LECs, the slope of the scalar form factor and the deviation of the Callan-Treiman theorem. Going beyond the SM and assuming the knowledge of the slope of the scalar form fact...

Matching is a relation between object types originally designed to support type-safe subclassing with binary methods. In this paper we generalize it to deal with general covariance by allowing eld and method parameter types to change covariantly in matching types. The result is a signiicant increase in the exibility of subclassing. The generalization is in a diierent direction than the recent p...

In 1891, Peterson [6] proved that every 3-regular bridge-less graph has a perfect matching. It is well known that the dual of a triangular mesh on a compact manifold is a 3-regular graph. M. Gopi and D. Eppstein [4] use Peterson’s theorem to solve the problem of constructing strips of triangles from triangular meshes on a compact manifold. P. Diaz-Gutierrez and M. Gopi [3] elaborate on the crea...

Template matching techniques are widely used in many computer vision tasks. Generally, a likelihood value is calculated from similarity measures, however the relation between these measures and the data likelihood is often incorrectly stated. It is clear that accurate likelihood estimation will improve the efficiency of the matching algorithms. This paper introduces a novel method for estimatin...

We introduce a concept of so-called disjoint ordering for any collection of finite sets. It can be viewed as a generalization of a system of distinctive representatives for the sets. It is shown that disjoint ordering is useful for network routing. More precisely, we show that Hall’s ‘marriage’ condition for a collection of finite sets guarantees the existence of a disjoint ordering for the set...

All graphs in this paper are understood to be finite, undirected, without loops or multiple edges. The graph G' = (V', E') is called an induced subgraph of G = (V, E) if V' ~ V and uv E E' if and only if {u, v} ~ V', uv E E. The following two problems about induced matchings have been formulated by Erdos and Nesetril at a seminar in Prague at the end of 1985: 1. Determine f(k, d), the maximum n...

A brick is a 3-connected graph such that the graph obtained from it by deleting any two distinct vertices has a perfect matching. Bricks are building blocks of the matching decomposition procedure of Kotzig, Lovasz and Plummer, and therefore many matching-related problems can be reduced to bricks. We prove, roughly, that every brick other than the Petersen graph can be generated from a “matchin...

Let G be a bipartite graph with positive integer weights on the edges and without isolated nodes. Let n, N and W be the node count, the largest edge weight and the total weight of G. Let k(x, y) be log x/ log(x/y). We present a new decomposition theorem for maximum weight bipartite matchings and use it to design an O( √ nW/k(n,W/N))-time algorithm for computing a maximum weight matching of G. T...