Semidefinite Programming and Ramsey Numbers

We use the theory of flag algebras to find new upper bounds for several small graph and hypergraph Ramsey numbers. In particular, we prove the exact values R(K−, K−, K−) = 28, R(K8, C5) = 29, R(K9, C6) = 41, R(Q3, Q3) = 13, R(K3,5, K1,6) = 17, R(C3, C5, C5) = 17, and R(K−, K−; 3) = 12, and in addition improve many additional upper bounds

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

Extremal and Ramsey Type Questions for Graphs and Ordered Graphs

In this thesis we study graphs and ordered graphs from an extremal point of view. In the first part of the thesis we prove that there are ordered forests H and ordered graphs of arbitrarily large chromatic number not containing such H as an ordered subgraph. In the second part we study pairs of graphs that have the same set of Ramsey graphs. We support a negative answer to the question whether there are pairs of non-isomorphic connected graphs that have this property. Finally we initiate the study of minimal ordered Ramsey graphs. For large families of ordered graphs we determine whether their members have finitely or infinitely many minimal ordered Ramsey graphs