{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:06:52Z","timestamp":1758823612790,"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>For a family of geometric objects in the plane $\\mathcal{F}=\\{S_1,\\ldots,S_n\\}$, define $\\chi(\\mathcal{F})$ as the least integer $\\ell$ such that the elements of $\\mathcal{F}$ can be colored with $\\ell$ colors, in such a way that any two intersecting objects have distinct colors. When $\\mathcal{F}$ is a set of pseudo-disks that may only intersect on their boundaries, and such that any point of the plane is contained in at most $k$ pseudo-disks, it can be proven that $\\chi(\\mathcal{F})\\le 3k\/2 + o(k)$ since the problem is equivalent to cyclic coloring of plane graphs. In this paper, we study the same problem when pseudo-disks are replaced by a family $\\mathcal{F}$ of pseudo-segments (a.k.a. strings) that do not cross. In other words, any two strings of $\\mathcal{F}$ are only allowed to \"touch\" each other. Such a family is said to be $k$-touching if no point of the plane is contained in more than $k$ elements of $\\mathcal{F}$. We give bounds on $\\chi(\\mathcal{F})$ as a function of $k$, and in particular we show that $k$-touching segments can be colored with $k+5$ colors. This partially answers a question of Hlin\u011bn\u00fd (1998) on the chromatic number of contact systems of strings.<\/jats:p>","DOI":"10.37236\/5710","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:08:19Z","timestamp":1578686899000},"source":"Crossref","is-referenced-by-count":2,"title":["Coloring Non-Crossing Strings"],"prefix":"10.37236","volume":"23","author":[{"given":"Louis","family":"Esperet","sequence":"first","affiliation":[]},{"given":"Daniel","family":"Gon\u00e7alves","sequence":"additional","affiliation":[]},{"given":"Arnaud","family":"Labourel","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,10,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:11:29Z","timestamp":1579237889000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i4p4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,14]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/5710","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,10,14]]},"article-number":"P4.4"}}