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W? s?w in ?l?ss th?t in bip?rtit? gr?phs th? m?ximum m?t?hing ?nd minimum v?rt?x ?ov?r h?v?...

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Advance Math

W? s?w in ?l?ss th?t in bip?rtit? gr?phs th? m?ximum m?t?hing?nd minimum v?rt?x ?ov?r h?v? th? s?m? siz?. (Th? numb?r of ?dg?sin th? m?t?hing ?qu?ls th? numb?r of v?rti??s in th? ?ov?r.)

(?)Find ?n ?x?mpl? of ? non-bip?rtit? gr?ph in whi?h th? minimumv?rt?x ?ov?r is ?x??tly twi?? ?s l?rg? ?s th? m?ximum m?t?hing.

(b)Find ?noth?r ?x?mpl? of ? non-bip?rtit? gr?ph in whi?h th?minimum v?rt?x ?ov?r ?nd th? m?ximum m?t?hing h?v? ?qu?l siz?s.

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