References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt147",{id:"formSmash:upper:j_idt147",widgetVar:"widget_formSmash_upper_j_idt147",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt148_j_idt150",{id:"formSmash:upper:j_idt148:j_idt150",widgetVar:"widget_formSmash_upper_j_idt148_j_idt150",target:"formSmash:upper:j_idt148:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

The Codegree Threshold for 3-Graphs with Independent NeighborhoodsPrimeFaces.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}); 2015 (English)In: SIAM Journal on Discrete Mathematics, ISSN 0895-4801, E-ISSN 1095-7146, Vol. 29, no 3, 1504-1539 p.Article in journal (Refereed) Published
##### Abstract [en]

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

2015. Vol. 29, no 3, 1504-1539 p.
##### Keyword [en]

codegree, Turan density, Turan function, 3-graphs
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-110602DOI: 10.1137/130926997ISI: 000362419600021OAI: oai:DiVA.org:umu-110602DiVA: diva2:865029
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt382",{id:"formSmash:j_idt382",widgetVar:"widget_formSmash_j_idt382",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt389",{id:"formSmash:j_idt389",widgetVar:"widget_formSmash_j_idt389",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt396",{id:"formSmash:j_idt396",widgetVar:"widget_formSmash_j_idt396",multiple:true});
Available from: 2015-10-26 Created: 2015-10-23 Last updated: 2015-10-26Bibliographically approved

Given a family of 3-graphs F, we define its codegree threshold coex(n, F) to be the largest number d = d(n) such that there exists an n-vertex 3-graph in which every pair of vertices is contained in at least d 3-edges but which contains no member of F as a subgraph. Let F-3,F-2 be the 3-graph on {a, b, c, d, e} with 3-edges abc, abd, abe, and cde. In this paper, we give two proofs that coex(n, {F-3,F-2}) = - (1/3 + o(1))n, the first by a direct combinatorial argument and the second via a flag algebra computation. Information extracted from the latter proof is then used to obtain a stability result, from which in turn we derive the exact codegree threshold for all sufficiently large n: coex(n, {F-3,F-2}) = [n/3] - 1 if n is congruent to 1 modulo 3, and [n/3] otherwise. In addition we determine the set of codegree-extremal configurations for all sufficiently large n.

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1090",{id:"formSmash:lower:j_idt1090",widgetVar:"widget_formSmash_lower_j_idt1090",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1091_j_idt1093",{id:"formSmash:lower:j_idt1091:j_idt1093",widgetVar:"widget_formSmash_lower_j_idt1091_j_idt1093",target:"formSmash:lower:j_idt1091:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});