Robert A. Getschmann
For a curriculum vitae please visit my LinkedIn Profile. I enjoy posting intersting science and technology articles on my Twitter Feed. Some public code and configurations that I share are at GitHub.
I graduated from the Rochester Institute of Technology earning a bachelor's degree and master's degree in Computer Science. While at RIT I was a member of Computer Science House.
My undergraduate concentration was in computer architecture and systems software (compilers, operating systems, networking). While a graduate student I concentrated in combinatorial computing, computational theory, and object oriented systems (with an emphasis on Smalltalk-80).
My Master's thesis involved the enumeration of various small Ramsey graphs. My thesis title was Enumeration of Small Triangle Free Ramsey Graphs. My advisor was Dr. Stanislaw Radziszowski. More thesis information can be found at the RIT Thesis Archive and below.
I am very interested in combinatorial computing, operating systems, mobile communications, networking systems, and object oriented systems. I had the privilege of presenting two discussions on BSD operating systems at the Boston Linux User Group in April of 2008, December of 2004, and October of 1999.
I spend the majority of my professionally oriented free time playing with the various free BSD UN*X like operating systems such as DragonFly BSD, FreeBSD, NetBSD, and OpenBSD.
In my free time I enjoy playing with Arduino, Go, Little Bits, and Smalltalk.
In 1930, a paper by Frank Plumpton Ramsey entitled ``On a Problem of Formal Logic'' appeared in the Proceedings of the London Mathematical Society. Although the impetus of this paper was one of mathematical logic, a far-reaching combinatorial result was needed by Ramsey to achieve his objective. This combinatorial result became known as Ramsey's Theorem.
One of the combinatorial structures which developed during the study of Ramsey's Theorem is that of a Ramsey graph. A Ramsey graph, denoted (k,l,n,e), is defined as an undirected graph that contains no cliques of size k, no independent sets of size l, with order n, and size e.
Knowledge of Ramsey graphs is useful in the improvement of bounds and sometimes the calculation of exact values for various Ramsey number parameter situations.
Straightforward enumeration of (k,l,n,e) Ramsey graphs for larger values of n is intractable with the current computing technology available. In order to produce such graphs, specialized algorithms need to be implemented.
This thesis provides the theoretical background developed by Graver and Yackel (1968), expanded upon by Grinstead and Roberts (1983), and generalized by Radziszowski and Kreher (1988) for the implementation of algorithms utilized for the enumeration of various Ramsey graphs.
An object-oriented graph manipulation package, including the above mentioned Ramsey graph enumeration algorithms, is implemented and documented. This package is utilized for the enumeration of all (3,3), (3,4), (3,5) and (3,6) Ramsey graphs. All minimum (3,7) graphs, all (3,7,22) critical Ramsey graphs, as well as many (3,8) and (3,9) Ramsey graphs are calculated.
The enumeration of the above mentioned graphs duplicates, verifies, and extends Ramsey graphs previously enumerated during other investigations.
I was able to enumerate all (3,3), (3,4), (3,5), and (3,6) Ramsey graphs. This work duplicated results obtained by Dr. Radziszowski.
The graph below is a (3,9,26,52) Ramsey graph that I enumerated. As far as I am aware it is the only (3,9,26,52) graph enumerated. Please correct me if new information is available.