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...

Imagine the situation: “One day, you notice an old country woman crossing a downtown street, just about to put one foot down on the rails of the streetcar line. [...] Suppose, now, that at the very moment she puts her foot on the rail a streetcar comes rushing down the tracks toward her. If the old woman does not notice the car and continues across the tracks nothing will happen. But if someone...

In the last decade there have been many results about special families of graphs whose number of perfect matchings is given by perfect or near perfect powers (N. Elkies et al., J. Algebraic Combin. 1 (1992), 111– 132; B.-Y. Yang, Ph.D. thesis, Department of Mathematics, MIT, Cambridge, MA, 1991; J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this pa...

In 1961, P.W. Kasteleyn enumerated the domino tilings of a 2n × 2n chessboard. His answer was always a square or double a square (we call such a number "squarish"), but he did not provide a combinatorial explanation for this. In the present thesis, we prove by mostly combinatorial arguments that the number of matchings of a large class of graphs with 4-fold rotational symmetry is squarish; our ...

A graph is a split graph if its vertices can be partitioned into a clique and a stable set. A graph is a k-split graph if its vertices can be partitioned into k sets, each of which induces a split graph. We show that the strong perfect graph conjecture is true for 2-split graphs and we design a polynomial algorithm to recognize a perfect 2-split graph.

The scratching of pen against paper signaled something at once mundane and momentous. “What is your name, your age, your residence?” asked Harvey Risk, a representative of the Southern Claims Commission. “My name is Mary Blackburn.... My age is about forty-fi ve years. My residence near Middlebrook,” the claimant responded. The commission awarded compensation for property losses during the Amer...

In this paper we propose an architecture for using crossorganization information sharing to identify members of a group of hosts enslaved for malicious purposes on the Internet. We root our system in so-called “detectives”— savvy network monitors like sophisticated intrusion detection systems or honeyfarms that have a deep understanding of malicious behavior. We augment information from these d...

The enforced migration of Africans to the Americas in conditions of slavery lasted from the middle of the sixteenth century until the 1860s and constituted the largest movement of people across the Atlantic until the middle of the nineteenth century. Referred to as the notorious “Middle Passage” because of the terrible conditions on board slave ships, this migration involved at least 12 million...

It is difficult to make sweeping statements about the status of women during the first century because there were exceptions to any characterization that might be made. However, there were laws, widely accepted codes, and assumptions regarding roles of women. These provide insight into the sort of life women lived during this period. As might be expected, there was a wide range of lifestyles fo...