{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:05Z","timestamp":1753893845955,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $k$ and $p$ be positive integers and let $Q$ be a finite point set in general position in the plane.\u00a0We say that $Q$ is $(k,p)$-Ramsey if there is a finite point set $P$ such that for every $k$-coloring $c$ of $\\binom{P}{p}$ there is a subset $Q'$ of $P$ such that $Q'$ and $Q$ have the same order type and $\\binom{Q'}{p}$ is monochromatic in $c$. Ne\u0161et\u0159il and Valtr proved that for every $k \\in \\mathbb{N}$, all point sets are $(k,1)$-Ramsey. They also proved that for every $k \\ge 2$ and $p \\ge 2$, there are point sets that are not $(k,p)$-Ramsey.As our main result, we introduce a new family of $(k,2)$-Ramsey point sets, extending a result of Ne\u0161et\u0159il and Valtr. We then use this new result to show that for every $k$ there is a point set $P$ such that no function $\\Gamma$ that maps ordered pairs of distinct points from $P$ to a set of size $k$ can satisfy the following \"local consistency\" property: if $\\Gamma$ attains the same values on two ordered triples of points from $P$, then these triples have the same orientation.\u00a0Intuitively, this implies that there cannot be such a function that is defined locally and determines the orientation of point triples.<\/jats:p>","DOI":"10.37236\/7039","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:43:30Z","timestamp":1578653010000},"source":"Crossref","is-referenced-by-count":0,"title":["Induced Ramsey-Type Results and Binary Predicates for Point Sets"],"prefix":"10.37236","volume":"24","author":[{"given":"Martin","family":"Balko","sequence":"first","affiliation":[]},{"given":"Jan","family":"Kyn\u010dl","sequence":"additional","affiliation":[]},{"given":"Stefan","family":"Langerman","sequence":"additional","affiliation":[]},{"given":"Alexander","family":"Pilz","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,10,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:42:42Z","timestamp":1579218162000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i4p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,20]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,10,5]]}},"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.37236\/7039","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,10,20]]},"article-number":"P4.24"}}