References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Simplicial complexes of graphs and hypergraphs with a bounded covering numberPrimeFaces.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);
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/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
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clickNode(panelWasOpen, childList[c]);
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if (!collapse && child.classList.contains('ui-corner-all')) {
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2005 (English)In: SIAM Journal on Discrete Mathematics, ISSN 0895-4801, E-ISSN 1095-7146, Vol. 19, no 3, 633-650 p.Article in journal (Refereed) Published
##### Abstract [en]

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

2005. Vol. 19, no 3, 633-650 p.
##### Keyword [en]

monotone graph property, simplicial homology, vertex cover, discrete Morse theory, discrete morse functions, connected graphs, decompositions, topology
##### Identifiers

URN: urn:nbn:se:kth:diva-15287ISI: 000234288300007ScopusID: 2-s2.0-33747155110OAI: oai:DiVA.org:kth-15287DiVA: diva2:333328
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt455",{id:"formSmash:j_idt455",widgetVar:"widget_formSmash_j_idt455",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt461",{id:"formSmash:j_idt461",widgetVar:"widget_formSmash_j_idt461",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
##### Note

QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

For 1 <= p <= n- 1, define Cov(n,p) as the family of graphs on the vertex set {1,..., n} with a covering number of at most p ( equivalently, with an independence number of at least n = p). Since the underlying vertex set is fixed, we may identify each graph in Cov(n,p) with its edge set. In particular, we may view Cov(n,p) as a simplicial complex. For i >= - 1, we show that the rank of the ith homology group of Cov(n,p) is a linear combination, with coefficients being polynomials in n, of the ranks of the ith homology groups of Cov(p+2, p),..., Cov(2p+1,p). Our proof takes place in a more general setting where we consider complexes of hypergraphs. In addition, we show that the (2p - 1)- skeleton of Cov(n,p) is shellable, which implies that Cov(n,p) is (2p - 2)-connected. For p <= 3, we give a complete description of the homology groups of Cov(n,p).

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});