{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:33Z","timestamp":1753893813958,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In a 2011 paper, Gy\u00e1rf\u00e1s\u00a0investigated a geometric Ramsey problem\u00a0on convex, separated, balanced, geometric $K_{n,n}$.\u00a0This led to appealing\u00a0extremal problem on square 0-1 matrices.\u00a0Gy\u00e1rf\u00e1s\u00a0conjectured that any 0-1 matrix of size $n\\times n$ has a staircase of size $n-1$.We introduce the non-symmetric version of Gy\u00e1rf\u00e1s' problem.\u00a0We give upper bounds and in certain range matching lower bound on\u00a0the corresponding extremal function.\u00a0In the square\/balanced case we improve the\u00a0$(4\/5+\\epsilon)n$ lower bound of Cai, Gy\u00e1rf\u00e1s\u00a0et al. to $5n\/6-7\/12$.\u00a0We settle the problem when instead of considering\u00a0maximum staircases we deal with the sum of the\u00a0size of the longest $0$- and $1$-staircases.<\/jats:p>","DOI":"10.37236\/5697","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T16:21:19Z","timestamp":1578673279000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Staircases of Gy\u00e1rf\u00e1s"],"prefix":"10.37236","volume":"23","author":[{"given":"J\u00e1nos","family":"Cs\u00e1nyi","sequence":"first","affiliation":[]},{"given":"Peter","family":"Hajnal","sequence":"additional","affiliation":[]},{"given":"G\u00e1bor V.","family":"Nagy","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,4,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:30:03Z","timestamp":1579221003000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,15]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5697","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,4,15]]},"article-number":"P2.17"}}