New Lower Bounds for Some Multicolored Ramsey Numbers

We use finite fields and extend a result of Fan Chung to give eight new, nontrivial, lower bounds.Comment: 6 page

Constructive Lower Bounds on Classical Multicolor Ramsey Numbers

This paper studies lower bounds for classical multicolor Ramsey numbers, first by giving a short overview of past results, and then by presenting several general constructions establishing new lower bounds for many diagonal and off-diagonal multicolor Ramsey numbers. In particular, we improve several lower bounds for R_k(4) and R_k(5) for some small k, including 415 \u3c = R_3(5), 634 \u3c = R_4(4), 2721 \u3c = R_4(5), 3416 \u3c = R_5(4) and 26082 \u3c = R_5(5). Most of the new lower bounds are consequences of general constructions

THE ELECTRONIC JOURNAL OF COMBINATORICS (2014), DS1.14 References

and Computing 11. The results of 143 references depend on computer algorithms. The references are ordered alphabetically by the last name of the first author, and where multiple papers have the same first author they are ordered by the last name of the second author, etc. We preferred that all work by the same author be in consecutive positions. Unfortunately, this causes that some of the abbreviations are not in alphabetical order. For example, [BaRT] is earlier on the list than [BaLS]. We also wish to explain a possible confusion with respect to the order of parts and spelling of Chinese names. We put them without any abbreviations, often with the last name written first as is customary in original. Sometimes this is different from the citations in other sources. One can obtain all variations of writing any specific name by consulting the authors database of Mathematical Reviews a

NCUWM Talk Abstracts 2010

Dr. Bryna Kra, Northwestern University “From Ramsey Theory to Dynamical Systems and Back” Dr. Karen Vogtmann, Cornell University “Ping-Pong in Outer Space” Lindsay Baun, College of St. Benedict Danica Belanus, University of North Dakota Hayley Belli, University of Oregon Tiffany Bradford, Saint Francis University Kathryn Bryant, Northern Arizona University Laura Buggy, College of St. Benedict Katharina Carella, Ithaca College Kathleen Carroll, Wheaton College Elizabeth Collins-Wildman, Carleton College Rebecca Dorff, Brigham Young University Melisa Emory, University of Nebraska at Omaha Avis Foster, George Mason University Xiaojing Fu, Clarkson University Jennifer Garbett, Kenyon College Nicki Gaswick, University of Nebraska-Lincoln Rita Gnizak, Fort Hays State University Kailee Gray, University of South Dakota Samantha Hilker, Sam Houston State University Ruthi Hortsch, University of Michigan Jennifer Iglesias, Harvey Mudd College Laura Janssen, University of Nebraska-Lincoln Laney Kuenzel, Stanford University Ellen Le, Pomona College Thu Le, University of the South Shauna Leonard, Arkansas State University Tova Lindberg, Bethany Lutheran College Lisa Moats, Concordia College Kaitlyn McConville, Westminster College Jillian Neeley, Ithaca College Marlene Ouayoro, George Mason University Kelsey Quarton, Bradley University Brooke Quisenberry, Hope College Hannah Ross, Kenyon College Karla Schommer, College of St. Benedict Rebecca Scofield, University of Iowa April Scudere, Westminster College Natalie Sheils, Seattle University Kaitlin Speer, Baylor University Meredith Stevenson, Murray State University Kiri Sunde, University of North Carolina Kaylee Sutton, John Carroll University Frances Tirado, University of Florida Anna Tracy, University of the South Kelsey Uherka, Morningside College Danielle Wheeler, Coe College Lindsay Willett, Grove City College Heather Williamson, Rice University Chengcheng Yang, Rice University Jie Zeng, Michigan Technological Universit

A lifting of graphs to 3-uniform hypergraphs, its generalization, and further investigation of hypergraph Ramsey numbers

Ramsey theory has posed many interesting questions for graph theorists that have yet to besolved. Many different methods have been used to find Ramsey numbers, though very feware actually known. Because of this, more mathematical tools are needed to prove exactvalues of Ramsey numbers and their generalizations. Budden, Hiller, Lambert, and Sanfordhave created a lifting from graphs to 3-uniform hypergraphs that has shown promise. Theybelieve that many results may come of this lifting, and have discovered some themselves.This thesis will build upon their work by considering other important properties of theirlifting and analogous liftings for higher-uniform hypergraphs. We also consider ways inwhich one may extend many known results in Ramsey Theory for graphs to the r-uniformhypergraph setting

problems in graph theory and probability

This dissertation is a study of some properties of graphs, based on four journal papers (published, submitted, or in preparation). In the first part, a random graph model associated to scale-free networks is studied. In particular, preferential attachment schemes where the selection mechanism is time-dependent are considered, and an infinite dimensional large deviations bound for the sample path evolution of the empirical degree distribution is found. In the latter part of this dissertation, (edge) colorings of graphs in Ramsey and anti-Ramsey theories are studied. For two graphs, G, and H, an edge-coloring of a complete graph is (G;H)-good if there is no monochromatic subgraph isomorphic to G and no rainbow (totally muticolored) subgraph isomorphic to H in this coloring. Some properties of the set of number of colors used by some (G;H)-colorings are discussed. Then the maximum element in this set when H is a cycle is studied