@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-T1J15DPM-T
  skos:prefLabel "graphe"@fr, "graph"@en ;
  a skos:Concept ;
  skos:narrower psr:-GZ5F8364-1 .

psr:-GZ5F8364-1
  dc:modified "2024-10-18"^^xsd:date ;
  skos:prefLabel "sous-graphe"@fr, "subgraph"@en ;
  skos:definition """En théorie des graphes, un <b>sous-graphe</b> est un graphe contenu dans un autre graphe. Formellement, un graphe <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 H=(V_{H},E_{H})}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>H</mi>         <mo>=</mo>         <mo stretchy="false">(</mo>         <msub>           <mi>V</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>H</mi>           </mrow>         </msub>         <mo>,</mo>         <msub>           <mi>E</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>H</mi>           </mrow>         </msub>         <mo stretchy="false">)</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle H=(V_{H},E_{H})}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7162bd3eb6d8843bcaa5de7d21ac9ef0bb12080" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.459ex; height:2.843ex;" alt="{\\\\displaystyle H=(V_{H},E_{H})}"></span> est un sous-graphe de <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 G=(V_{G},E_{G})}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>G</mi>         <mo>=</mo>         <mo stretchy="false">(</mo>         <msub>           <mi>V</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>G</mi>           </mrow>         </msub>         <mo>,</mo>         <msub>           <mi>E</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>G</mi>           </mrow>         </msub>         <mo stretchy="false">)</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle G=(V_{G},E_{G})}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41ea36cd1c086521dc035b33ecd879ad9cd0109e" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.887ex; height:2.843ex;" alt="{\\\\displaystyle G=(V_{G},E_{G})}"></span> si <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 V_{H}\\\\subseteq V_{G}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>V</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>H</mi>           </mrow>         </msub>         <mo>⊆<!-- ⊆ --></mo>         <msub>           <mi>V</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>G</mi>           </mrow>         </msub>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle V_{H}\\\\subseteq V_{G}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11ccaff290c9de010a9c7abc0e4a077f8c5719ad" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.024ex; height:2.509ex;" alt="{\\\\displaystyle V_{H}\\\\subseteq V_{G}}"></span>  et <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_{H}\\\\subseteq \\\\{(x,y)\\\\in E_{G}\\\\mid x\\\\in V_{H}\\\\wedge y\\\\in V_{H}\\\\}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>E</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>H</mi>           </mrow>         </msub>         <mo>⊆<!-- ⊆ --></mo>         <mo fence="false" stretchy="false">{</mo>         <mo stretchy="false">(</mo>         <mi>x</mi>         <mo>,</mo>         <mi>y</mi>         <mo stretchy="false">)</mo>         <mo>∈<!-- ∈ --></mo>         <msub>           <mi>E</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>G</mi>           </mrow>         </msub>         <mo>∣<!-- ∣ --></mo>         <mi>x</mi>         <mo>∈<!-- ∈ --></mo>         <msub>           <mi>V</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>H</mi>           </mrow>         </msub>         <mo>∧<!-- ∧ --></mo>         <mi>y</mi>         <mo>∈<!-- ∈ --></mo>         <msub>           <mi>V</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>H</mi>           </mrow>         </msub>         <mo fence="false" stretchy="false">}</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle E_{H}\\\\subseteq \\\\{(x,y)\\\\in E_{G}\\\\mid x\\\\in V_{H}\\\\wedge y\\\\in V_{H}\\\\}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/647eab230132c7100be7a691e8ffa9c9dd65800c" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.018ex; height:2.843ex;" alt="{\\\\displaystyle E_{H}\\\\subseteq \\\\{(x,y)\\\\in E_{G}\\\\mid x\\\\in V_{H}\\\\wedge y\\\\in V_{H}\\\\}}"></span>. L'ensemble des sommets du sous-graphe <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 H}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>H</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle H}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\\\\displaystyle H}"></span> est un sous-ensemble de l'ensemble des sommets de <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 G}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>G</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle G}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\\\\displaystyle G}"></span> et l'ensemble des arcs de <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 H}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>H</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle H}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\\\\displaystyle H}"></span> est un sous-ensemble de l'ensemble des arcs de <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 G}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>G</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle G}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\\\\displaystyle G}"></span> ayant leur origine et leur extrémité parmi les sommets de <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 H}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>H</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle H}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\\\\displaystyle H}"></span>.  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Sous-graphe">https://fr.wikipedia.org/wiki/Sous-graphe</a>)"""@fr, """A subgraph of a graph G is another graph formed from a subset of the vertices and edges of G. The vertex subset must include all endpoints of the edge subset, but may also include additional vertices. A spanning subgraph is one that includes all vertices of the graph; an induced subgraph is one that includes all the edges whose endpoints belong to the vertex subset. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Glossary_of_graph_theory#subgraph">https://en.wikipedia.org/wiki/Glossary_of_graph_theory#subgraph</a>)"""@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Sous-graphe>, <https://en.wikipedia.org/wiki/Glossary_of_graph_theory#subgraph> ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-T1J15DPM-T .