References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt155",{id:"formSmash:upper:j_idt155",widgetVar:"widget_formSmash_upper_j_idt155",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt156_j_idt159",{id:"formSmash:upper:j_idt156:j_idt159",widgetVar:"widget_formSmash_upper_j_idt156_j_idt159",target:"formSmash:upper:j_idt156: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});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
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
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt399",{id:"formSmash:j_idt399",widgetVar:"widget_formSmash_j_idt399",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt406",{id:"formSmash:j_idt406",widgetVar:"widget_formSmash_j_idt406",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt412",{id:"formSmash:j_idt412",widgetVar:"widget_formSmash_j_idt412",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_idt700:0:j_idt705",widgetVar:"overlay413324",target:"formSmash:j_idt700:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1138",{id:"formSmash:lower:j_idt1138",widgetVar:"widget_formSmash_lower_j_idt1138",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1139_j_idt1141",{id:"formSmash:lower:j_idt1139:j_idt1141",widgetVar:"widget_formSmash_lower_j_idt1139_j_idt1141",target:"formSmash:lower:j_idt1139:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});