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References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

On avoiding some families of arraysPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2012 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 312, no 5, 963-972 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2012. Vol. 312, no 5, 963-972 p.
##### Keyword [en]

Latin square, avoiding arrays, list coloring
##### National Category

Discrete Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-43325DOI: 10.1016/j.disc.2011.10.028OAI: oai:DiVA.org:umu-43325DiVA: diva2:413024
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt381",{id:"formSmash:j_idt381",widgetVar:"widget_formSmash_j_idt381",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2011-04-28 Created: 2011-04-27 Last updated: 2012-05-23Bibliographically approved
##### In thesis

An *n*×*n* array *A* with entries from {1,…,*n*} is *avoidable* if there is an *n*×*n* Latin square *L* such that no cell in *L* contains a symbol that occurs in the corresponding cell in *A*. We show that the problem of determining whether an array that contains at most two entries per cell is avoidable is *NP*-complete, even in the case when the array has entries from only two distinct symbols. Assuming that *P*≠*NP*, this disproves a conjecture by Öhman. Furthermore, we present several new families of avoidable arrays. In particular, every single entry array (arrays where each cell contains at most one symbol) of order *n*≥2*k* with entries from at most *k* distinct symbols and where each symbol occurs in at most *n*−2 cells is avoidable, and every single entry array of order *n*, where each of the symbols 1,…,*n* occurs in at most cells, is avoidable. Additionally, if *k*≥2, then every single entry array of order at least *n*≥4, where at most *k* rows contain non-empty cells and where each symbol occurs in at most *n*−*k*+1 cells, is avoidable.

1. On some graph coloring problems$(function(){PrimeFaces.cw("OverlayPanel","overlay413324",{id:"formSmash:j_idt647:0:j_idt651",widgetVar:"overlay413324",target:"formSmash:j_idt647:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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