Metric random matchings with applications

Thresholds for Matchings in Random Bipartite Graphs with Applications to Hashing-Based Data Structures

The number of maximal matchings in polyphenylene chains

A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also de...

Stable Matchings in Metric Spaces: Modeling Real-World Preferences using Proximity

Suppose each of n men and n women is located at a point in a metric space. A woman ranks the men in order of their distance to her from closest to farthest, breaking ties at random. Œe men rank the women similarly. An interesting problem is to use these ranking lists and €nd a stable matching in the sense of Gale and Shapley. Œis problem formulation naturally models preferences in several real ...

Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications

In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the  assumption of normality we establish common fixed point theorems for the generalized quasi-contractions  with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$  in the set...

Perfect Matchings in Edge-Transitive Graphs

We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...