{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article10456","name":"Conflict-Free Coloring of Intersection Graphs","abstract":"A conflict-free k-coloring of a graph G=(V,E) assigns one of k different colors to some of the vertices such that, \r\nfor every vertex v, there is a color that is assigned to exactly one vertex among v and v's neighbors. \r\nSuch colorings have applications in wireless networking, robotics, and geometry, and are well studied in graph theory.\r\nHere we study the conflict-free coloring of geometric intersection graphs. \r\nWe demonstrate that the intersection graph of n geometric objects without fatness properties and size restrictions may have conflict-free chromatic number in \\Omega(log n\/log log n) and in \\Omega(\\sqrt{\\log n}) for disks or squares of different sizes; \r\nit is known for general graphs that the worst case is in \\Theta(log^2 n). \r\nFor unit-disk intersection graphs, we prove that it is NP-complete\r\nto decide the existence of a conflict-free coloring\r\nwith one color; we also show that six colors always suffice,\r\nusing an algorithm that colors unit disk graphs of restricted height with two colors. \r\nWe conjecture that four colors are sufficient, which we prove for unit squares instead of unit disks.\r\nFor interval graphs, we establish a tight worst-case bound of two.","keywords":["conflict-free coloring","intersection graphs","unit disk graphs","complexity","worst-case bounds"],"author":[{"@type":"Person","name":"Fekete, S\u00e1ndor P.","givenName":"S\u00e1ndor P.","familyName":"Fekete"},{"@type":"Person","name":"Keldenich, Phillip","givenName":"Phillip","familyName":"Keldenich"}],"position":31,"pageStart":"31:1","pageEnd":"31:12","dateCreated":"2017-12-07","datePublished":"2017-12-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Fekete, S\u00e1ndor P.","givenName":"S\u00e1ndor P.","familyName":"Fekete"},{"@type":"Person","name":"Keldenich, Phillip","givenName":"Phillip","familyName":"Keldenich"}],"copyrightYear":"2017","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ISAAC.2017.31","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6295","volumeNumber":92,"name":"28th International Symposium on Algorithms and Computation (ISAAC 2017)","dateCreated":"2017-12-07","datePublished":"2017-12-07","editor":[{"@type":"Person","name":"Okamoto, Yoshio","givenName":"Yoshio","familyName":"Okamoto"},{"@type":"Person","name":"Tokuyama, Takeshi","givenName":"Takeshi","familyName":"Tokuyama"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article10456","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6295"}}}