The White mountains in American literature of the nineteenth century

Thesis (M.A.)--Boston University, 1945. This item was digitized by the Internet Archive

Finding Aid for the John Sharp Williams Collection (MUM00480)

This collection contains research material accumulated by historian George Coleman Osborn while researching his biographies John Sharp Williams: Planter-Statesman of the Deep South (1943) and James Kimble Vardaman: Southern Commoner (1981). These research files include transcripts of both Williams and Vardaman correspondence; typed excerpts from the Congressional Record and various newspapers; photographs; as well as broadsheets, clippings, and other printed material

R(W5 , K5) = 27

The two-color Ramsey number R(G , H) is defined to be the smallest integer n such that any graph F on n vertices contains either a subgraph isomorphic to G or the complement of F contains a subgraph isomorphic to H. Ramsey numbers serve to quantify many of the existing theorems of Ramsey theory, which looks at large combinatorial objects for certain given smaller combinatorial objects that must be present. In 1989 George R. T. Hendry presented a table of two-color Ramsey numbers R(G , H) for all pairs of graphs G and H having at most five vertices. This table left seven unsolved cases, of which three have since been solved. This thesis eliminates one of the remaining four cases, R(W5 , K5), where a K5 is the complete graph on five vertices and a W5 is a wheel of order 5, which can be pictured as a wheel having four spokes or as a cycle of length 4 having all four vertices adjacent to a central vertex. In this thesis we show R(W5, K5) to be equal to 27, utilizing a combinatorial approach with significant computations. Specifically we use a technique developed by McKay and Radziszowski to effectively glue together smaller graphs in an effort to prove exhaustively that no graph having 27 vertices exists that does not contain an independent set on five vertices or a subgraph isomorphic to W5. The previous best bounds for this case were 27 \u3c= R( W_5 , K_5 ) \u3c= 29

History of the Indiana State Teachers College

Not Available.Max P. AllenNot ListedNot ListedMaster of ArtsDepartment Not ListedCunningham Memorial library, Terre Haute, Indiana State University.isua-thesis-1931-allenMastersTitle from document title page. Document formatted into pages: contains 129p. : ill. Includes annotated bibliography

An algorithmic approach for multi-color Ramsey graphs

The classical Ramsey number R(r1,r2,...,rm) is defined to be the smallest integer n such that no matter how the edges of Kn are colored with the m colors, 1, 2, 3, . . . ,m, there exists some color i such that there is a complete subgraph of size ri, all of whose edges are of color i. The problem of determining Ramsey numbers is known to be very difficult and is usually split into two problems, finding upper and lower bounds. Lower bounds can be obtained by the construction of a, so called, Ramsey graph. There are many different methods to construct Ramsey graphs that establish lower bounds. In this thesis mathematical and computational methods are exploited to construct Ramsey graphs. It was shown that the problem of checking that a graph coloring gives a Ramsey graph is NP-complete. Hence it is almost impossible to find a polynomial time algorithm to construct Ramsey graphs by searching and checking. Consequently, a method such as backtracking with good pruning techniques should be used. Algebraic methods were developed to enable such a backtrack search to be feasible when symmetry is assumed. With the algorithm developed in this thesis, two new lower bounds were established: R(3,3,5)≥45 and R(3,4,4)≥55. Other best known lower bounds were matched, such as R(3,3,4)≥30. The Ramsey graphs giving these lower bounds were analyzed and their full symmetry groups were determined. In particular it was shown that there are unique cyclic graphs up to isomorphism giving R(3,3,4)≥30 and R(3,4,4)≥55, and 13 non-isomorphic cyclic graphs giving R(3,3,5)≥45

Muscogiana Vol. 19(2), Fall 2008

https://csuepress.columbusstate.edu/muscogiana/1041/thumbnail.jp

Centennial Bibliography On The History Of American Sociology

THE CENTENNIAL BIBLIOGRAPHY ON THE HISTORY OF AMERICAN SOCIOLOGY is intended as an inclusive clearinghouse for sources, studies, and other references that illuminate the origins and subsequent development of the sociological enterprise in the United States of America.2 As such, this bibliography is necessarily provisional and is envisioned as an on-going project to which further citations may be added as they are discovered and as new works are published. Due to the enormous scope of the project, and the short time frame within which the initial compilation was completed, countless useful and insightful references have been unintentionally omitted. Some portions of the citations are currently more comprehensive than others. Gaps, holes, and inexplicable lapses are the sole responsibility of the compiler, for which he not so much apologetic as he is determined to repair them. The assistance of each reader of this bibliography is earnestly enlisted to supply additional references with which they are familiar. Likewise, the current bibliography undoubtedly contains bibliographic errors due in part to the sheer impracticality of physically checking each and every item referenced herein. Again, the assistance of bibliographically astute readers is heartily enlisted to correct such errors. Readers wishing to report errors or to nominate additional candidates for inclusion in future updates of this bibliography are warmly invited to communicate corrections or recommendations together with brief explanations and complete bibliographic particulars via email to: [email protected]