Tím jsme dokázali, ¾e celková slo¾itost Dinicova algoritmu pro jednotkové
kapacity je $\O(m^{3/2})$. Tím jsme si pomohli pro øídké grafy.
+\vbox{
+\vbox to 0pt{\vskip 2ex\rightline{\epsfxsize=0.2\hsize\epsfbox{dinic-vrcholrez.eps}}\vss}\vskip-\baselineskip
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\s{Jednotkové kapacity a jeden ze stupòù roven 1:}
Úlohu hledání maximálního párování v~bipartitním grafu, pøípadnì hledání
vrcholovì disjunktních cest v~obecném grafu lze pøevést (viz pøedchozí kapitola)
nebo výstupní stupeò roven jedné.
Pro takovou sí» mù¾eme pøedchozí odhad je¹tì tro¹ku upravit. Pokusíme
se nalézt v síti po~$k$~krocích nìjaký malý øez. Místo rozhraní budeme hledat jednu malou
-vrstvu a z malé vrstvy vytvoøíme malý øez tak, ¾e pro ka¾dý vrchol z vrstvy vezmeme tu hranu,
+vrstvu a z~malé vrstvy vytvoøíme malý øez tak, ¾e pro ka¾dý vrchol z~vrstvy vezmeme tu hranu,
která je ve svém smìru sama.
-\figure{dinic-vrcholrez.eps}{Øez podle vrcholù ve vrstvì}{0.2\hsize}
+}
Po $k$ krocích máme alespoò $k$ vrstev, a~proto existuje vrstva $\delta$ s nejvý¹e $n/k$ vrcholy.
Tedy existuje øez $C$ o~velikosti $\vert C\vert \leq n/k$ (získáme z vrstvy $\delta$ vý¹e popsaným postupem).
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