Math482lecture19inclassex.solns - a Øh48Ô Ö iÒg Ò Ða...

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Unformatted text preview: a Øh48Ô Ö iÒg Ò Ða ××eÜ eÖ i×e × a fØeÖØe ×Ø ÖaØ ieÔ ÖÓb ÐeÑ × ;Øh e×ea ÖeÒÓ ØØÓb e×ÙbÑ iØØed fÓ Ög Öad iÒg h eÖedÓÛ eÙ ×eØh e faØØha ØÛ ehÓ ×e b ≥ iÒ P Ó fØh egeÒ eÖa ÐÔ Ö iÑ a ÐdÙa Ða ÐgÓ Ö iØhÑ ? Ó ÐÙ ØiÓÒ eÒ eed b ≥ ×Ó Øha ØØh ea ÖØ iia ÐÚa Ö iab Ðe× iÒ Øh eÖe×ØÖ iØedÔ Ö iÑ a ÐÔ ÖÓb ÐeÑ RP Ó ÖÖe×ÔÓÒd ØÓaba × ifea × ib Ðe×Ó ÐÙ Ø iÓÒ hÓÛ hÓÛ Øh eF Ó ÖdF Ù Ðk eÖ×ÓÒa ÐgÓ Ö iØhÑ aÒb eaÔÔ Ðied ØÓ Øh ea ×eÛ h eÖeaÔa iØ ie×a ÖeÔÙ ØÓÒ Øh e ÒÓde× Ó faÓÛ Ò e ØÛ Ó Ök Ó ÐÙ ØiÓÒ G iÚ eÒad ig ÖaÔh G Û iØhÛ e igh Ø× b i ÓÒ Øh eÒÓd e×Û eÓÒ ×ØÖÙ ØaÒ eÛ d ig ÖaÔh G ′ iÒ Øh e fÓ ÐÐÓÛ iÒgÛ aÝ :F Ó ÖeahÚ eÖØeÜ v iÒ G Û eÖea ØeØÛ ÓÚ eÖØ ie× v + aÒd v − iÒ G ′ aÒdÛ eÔÙ Øa × iÒg Ðe d iÖeØed edge fÖÓÑ v − ØÓ v + Û iØhaÔa iØÝ b v F Ó Öeahd iÖeØededge ( v, w ) Ó f G Û eaddaÒ edgeÓ f Øh e fÓ ÖÑ ( v + , w − ) Û iØh iÒÒ iØeaÔa iØÝ ØÓ G ′ eÒÓÛ aÔÔ ÐÝF Ó ÖdF Ù Ðk eÖ×ÓÒ ØÓÒdaÑ aÜ iÑ a ÐÓÛ f ′ fÖÓÑ s − ØÓ t + f ′ Ó ÖÖe×ÔÓÒd ×ØÓaÓÛ f iÒ G bÝ Öe×ØÖ iØ iÒg f ′ ØÓ Øh eedge×Ó f G eÐa iÑ Øha Ø f i×aÑ aÜ iÑ a ÐÓÛ iÒ G C Ðea Ö ÐÝ f i×a fea × ib ÐeÓÛ × iÒeØh eÓÛ Øh ÖÓÙgh v i×eÜaØ ÐÝ Øh eÓÛ Øh ÖÓÙgh Øh ea Ö ( v − , v + ) iÒ G ′ Û h ih i×a ØÑ Ó ×Ø b v fØh eÖeeÜ i×ØedaÓÛ h iÒ G Ó fg Öea ØeÖ Úa ÐÙ eØhaÒ f Øh eÒÛ eaÒÓÒ ×ØÖÙ ØaÓÛ h ′ iÒ G ′ Û iØh Øh e×aÑ eÚa ÐÙ ea × h bÝÔÙ ØØ iÒgÓÛ h j ÓÒ ØÓ edge×Ó f G ′ Øha Øa Ð×ÓeÜ i×Ø iÒ G aÒd Øh...
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This note was uploaded on 02/19/2012 for the course MATH 482 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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Math482lecture19inclassex.solns - a Øh48Ô Ö iÒg Ò Ða...

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