@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr:-LH52F1PH-M
  skos:prefLabel "arête transversale"@fr, "vertex cover"@en ;
  a skos:Concept ;
  skos:broader psr:-D3KFB368-T .

psr:-QFN1T51G-V
  skos:prefLabel "Kruskal-Katona theorem"@en, "théorème de Kruskal-Katona"@fr ;
  a skos:Concept ;
  skos:broader psr:-D3KFB368-T .

psr: a skos:ConceptScheme .
psr:-J8SLM0HB-6
  skos:prefLabel "graph theory"@en, "théorie des graphes"@fr ;
  a skos:Concept ;
  skos:narrower psr:-D3KFB368-T .

psr:-D3KFB368-T
  skos:broader psr:-J8SLM0HB-6 ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Hypergraphe>, <https://en.wikipedia.org/wiki/Hypergraph> ;
  skos:definition """Les hypergraphes sont des objets mathématiques généralisant la notion de graphe. Ils ont été nommés ainsi par Claude Berge dans les années 1960. Les hypergraphes généralisent la notion de graphe non orienté dans le sens où les arêtes ne relient plus un ou deux sommets, mais un nombre quelconque de sommets (compris entre un et le nombre de sommets de l’hypergraphe). 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Hypergraphe">https://fr.wikipedia.org/wiki/Hypergraphe</a>)"""@fr, """In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices. Formally, a <b>directed hypergraph</b> is a pair <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle (X,E)}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mo stretchy="false">(</mo>
         <mi>X</mi>
         <mo>,</mo>
         <mi>E</mi>
         <mo stretchy="false">)</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle (X,E)}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09abc2916dda67f75618cdfa4d8c79c631ed013e" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.599ex; height:2.843ex;" alt="(X,E)"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle X}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>X</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle X}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="X"></span> is a set of elements called <i>nodes</i>, <i>vertices</i>, <i>points</i>, or <i>elements</i> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle E}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>E</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle E}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="E"></span> is a set of pairs of subsets of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle X}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>X</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle X}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="X"></span>. Each of these pairs <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle (D,C)\\\\in E}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mo stretchy="false">(</mo>
         <mi>D</mi>
         <mo>,</mo>
         <mi>C</mi>
         <mo stretchy="false">)</mo>
         <mo>∈<!-- ∈ --></mo>
         <mi>E</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle (D,C)\\\\in E}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c074906f49a4a3a38b843056fdb86e4fc42d264" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.15ex; height:2.843ex;" alt="{\\\\displaystyle (D,C)\\\\in E}"></span> is called an <i>edge</i> or <i>hyperedge</i>;  the vertex subset <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle D}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>D</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle D}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="D"></span> is known as its <i>tail</i> or <i>domain</i>, and  <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle C}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>C</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle C}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="C"></span> as its  <i>head</i> or <i>codomain</i>.
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Hypergraph">https://en.wikipedia.org/wiki/Hypergraph</a>)"""@en ;
  skos:inScheme psr: ;
  skos:prefLabel "hypergraphe"@fr, "hypergraph"@en ;
  a skos:Concept ;
  skos:narrower psr:-QFN1T51G-V, psr:-LH52F1PH-M .