A matching in a graph G is a subset M of the edges of G such that no two share an endpoint. A matching has maximum cardinality if its cardinality is at least as large as that of any other matching. An odd-set cover OSC of a graph G is a labeling of the nodes of G with integers such that every edge of G is either incident to a node labeled 1 or connects two nodes labeled with the same number i ≥...

The Induced H-Matching problem asks to find k disjoint, induced subgraphs isomorphic to H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes the classical Independent Set and Induced Matching problems, among several other problems. We show that Induced H-Matching is fixed-parameter tractable in k on claw-free graphs when H is a fixe...

We study many–to–one matching markets where hospitals have responsive preferences over students. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling. Roth and Sotomayor (1990) showed that equilibrium outcomes can be unstable. We prove that any stable matching is obtained in some equilibrium. We ...

Several structural results for the set of competitive equilibria in trading networks with frictions are established: The lattice theorem, rural hospitals existence side‐optimal equilibria, and a group‐incentive‐compatibility result hold imperfectly transferable utility presence frictions. While our developed network model, they also imply analogous (and new) exchange economies combinatorial dem...

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

A zircon is a poset in which every principal order ideal is finite and equipped with a so-called special matching. We prove that the subposet induced by the fixed points of any automorphism of a zircon is itself a zircon. This provides a natural context in which to view recent results on Bruhat orders on twisted involutions in Coxeter groups. 1. Background and results Let P be a partially order...

In this report, we show that an arbitrarily given quadrilateral can always be interpreted as an image of a parallelogram and that the interpretation is unique aside from a multiplicative constant. Several applications of this theorem are discussed. It could be used to prove an old, geometrical theorem; it could facilitate the matching process when a sequence of images are available; it could be...

In this paper, we prove correctness of parallelizing a string matcher using Haskell as a theorem prover. We use refinement types to specify correctness properties, Haskell terms to express proofs and Liquid Haskell to check correctness of proofs. First, we specify and prove that a class of monoid morphisms can be parallelized via parallel monoid concatenation. Then, we encode string matching as...