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

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

New lower bounds for Ramsey numbers of graphs and hypergraphs

Dedicated to the memory of Rodica Simion Let G be an r-uniform hypergraph. The multicolor Ramsey number rk(G) is the minimum n such that every k-coloring of the edges of the complete r-uniform hypergraph K (r) n monochromatic copy of G. Improving slightly upon results from [1], we prove that tk 2 + 1 ≤ rk(K2,t+1) ≤ tk 2 + k + 2, yields a where the lower bound holds when t and k are both powers of a prime p. When t = 1, we improve the lower bound by 1, proving that rk(C4) ≥ k 2 + 2 for any prime power k. extends the result of [11] which proves the same bound when k is an odd prime power. These results are generalized to hypergraphs in the following sense. Fix integers r, s, t ≥ 2. Let H (r) (s, t) be the complete r-partite r-graph with r − 2 parts of size 1, one part of size s, and one part of size t (note that H (2) (s, t) = Ks,t). We prove tk 2 − k + 1 ≤ rk(H (r) (2, t + 1)) ≤ tk 2 + k + r, where the lower bound holds when t and k are both powers of a prime p; and k s − k s−1 ≤ rk(H (r) (s, t)) ≤ O(k s), for fixed t, s ≥ 2, t> (s − 1)!; rk(H (r) (3, 3)) = (1 + o(1))k 3, where the lower bound holds when k is a prime power. Some of our lower bounds are special cases of a family of more general hypergraph constructions obtained by algebraic methods. We describe these, thereby extending results of [12] about graphs