7 research outputs found
Independent arithmetic progressions
We show that there is a positive constant such that any graph on vertex
set with at most edges contains an independent set of
order whose vertices form an arithmetic progression. We also present
applications of this result to several questions in Ramsey theory.Comment: 4 page
Independent arithmetic progressions
We show that there is a positive constant c such that any graph on vertex set [n] with at most cn^(2)/k^(2) log k edges contains an independent set of order k whose vertices form an arithmetic progression. We also present applications of this result to several questions in Ramsey theory
Short proofs of some extremal results III
We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are reasonably short
Short proofs of some extremal results III
We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are reasonably short