Video: Puas yog daim duab bipartite txuas?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
1 Teb. Txuas bipartite graph yog a daim duab Ua tiav ob qho tib si, cov xwm txheej hauv qab no: Vertices tuaj yeem muab faib ua ob qhov sib txawv U thiab V (uas yog, U thiab V yog txhua qhov kev ywj pheej) xws li txhua qhov ntug hauv graph txuas ib tug vertex nyob rau hauv U rau ib tug nyob rau hauv V.
Ib yam li ib tug yuav nug, ua li cas koj thiaj paub tias daim duab yog bipartite?
Yog li yog koj tuaj yeem 2-xim koj daim duab , nws yuav bipartite . Kom meej meej, yog koj muaj daim duab peb sab, koj xav tau 3 xim xim rau nws. Thaum twg koj muaj 2 xim, ob chav xim (liab vertices, xiav vertices), muab rau koj bipartization. A graph yog bipartite yog tias thiab xwb yog tsis muaj ib lub voj voog khib hauv lub daim duab.
Tsis tas li ntawd, txhua tsob ntoo puas yog daim duab bipartite? Muaj ib txoj hauv kev tshwj xeeb ntawm ib qho 2 vertices hauv a tsob ntoo . Txhua tsob ntoo nrog tsawg kawg 2 vertices muaj tsawg kawg yog 2 vertices ntawm degree 1. Txhua tsob ntoo yog bipartite . Tshem tawm ib qho ntug ntawm a tsob ntoo yuav cais cov tsob ntoo nyob rau hauv 2 txuas txuas.
Ntxiv rau qhov no, nws txhais li cas rau daim duab ua bipartite?
Hauv kev ua lej ntawm daim duab txoj kev xav, a daim duab bipartite (los yog bigraph) yog a daim duab nws vertices yuav muab faib ua ob disjoint thiab ywj siab teev thiab xws li hais tias txhua ntug txuas ib tug vertex rau ib tug nyob rau hauv. Vertex teeb thiab. feem ntau hu ua qhov chaw ntawm lub daim duab.
Dab tsi yog qhov txawv ntawm bipartite graph thiab tiav bipartite graph?
A daim duab bipartite G muaj ib txheej ntawm vertices V uas yog disjoint union ntawm ob pawg A thiab B thiab tag nrho cov npoo hauv G muaj ib kawg. hauv A thiab ib qho kawg hauv B. G yog ua kom tiav yog tias txhua ntug ntawm A mus rau B yog hauv daim duab . Cov txawv yog hauv lo lus "txhua".
Pom zoo:
Vim li cas nws thiaj li hais tias lub Orthocenter ntawm daim duab peb sab obtuse yuav tsum nyob rau sab nraud ntawm daim duab peb sab?
Nws hloov tawm tias tag nrho peb qhov siab ib txwm sib tshuam ntawm tib lub ntsiab lus - lub npe hu ua orthocenter ntawm daim duab peb sab. Lub orthocenter tsis yog ib txwm nyob hauv daim duab peb sab. Yog tias daim duab peb sab yog obtuse, nws yuav nyob sab nraud. Txhawm rau ua kom qhov no tshwm sim cov kab qhov siab yuav tsum tau txuas ntxiv kom lawv hla
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Dab tsi yog qhov txawv ntawm lub xeev daim duab kos duab thiab daim duab ua haujlwm?
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Nws txhais li cas rau daim duab ua bipartite?
Nyob rau hauv kev ua lej ntawm daim duab txoj kev xav, ib daim duab bipartite (lossis bigraph) yog ib daim duab uas nws cov vertices tuaj yeem muab faib ua ob pawg disjoint thiab ywj siab thiab xws li tias txhua ntug txuas ib lub vertex rau ib qho hauv. Vertex teev thiab. feem ntau hu ua qhov chaw ntawm daim duab
Puas yog daim duab nrog ib qho vertex bipartite?
Ib daim duab bipartite yog ib qho uas nws qhov vertices, V, tuaj yeem muab faib ua ob pawg ywj pheej, V1 thiab V2, thiab txhua tus ntug ntawm daim duab txuas ib qho vertex hauv V1 mus rau ib qho vertex hauv V2 (Skiena 1990). Yog tias txhua qhov vertex ntawm V1 txuas nrog txhua qhov vertex ntawm V2 daim duab hu ua tiav bipartite graph