From 56b740565fd6467564be28b5465ad24cccf71109 Mon Sep 17 00:00:00 2001 From: Holden Rohrer Date: Thu, 16 Jan 2020 21:24:46 -0500 Subject: moved comb hw --- tech-math/ws6.tex | 29 ----------------------------- 1 file changed, 29 deletions(-) delete mode 100644 tech-math/ws6.tex (limited to 'tech-math/ws6.tex') diff --git a/tech-math/ws6.tex b/tech-math/ws6.tex deleted file mode 100644 index 5042920..0000000 --- a/tech-math/ws6.tex +++ /dev/null @@ -1,29 +0,0 @@ -\def\pre#1{\leavevmode\llap{\hbox to \parindent{\hfil #1 \hfil}}} - -\noindent {\bf Q1)} %#14:2 - -Considering a flow from Source $S$ which is connected to all members of $V_1$ and a similar sink $T$ with respect to $V_2$, this can be solved by the Ford-Fulkerson algorithm. - -Let $V_{kj}$ be the $j^{th}$ member, from left to right of $V_k$. The optimum matching is $$\{V_11\to V_22, V_12\to V_27, V_13\to V_25, V_14\to V_21, V_15\to V_26, V_17\to V_24\}$$ because the Ford-Fulkerson algorithm halts, and Hall's theorem holds: there is a grouping of vertices in $V_1$ with a fewer number of neighbors than in the group. - -\noindent {\bf Q2)} %#14:8 - -$w=3$. - -Antichain: $\{x_1,x_2,x_3\}$. - -Chain Partition: $\{x_3,x_4,x_5\}\cup\{x_6,x_1\}\cup\{x_2\}$. - -\noindent {\bf Q3)} %#15:2 - -\let\sp\thinspace -$$\pi_1\pi_2 = \left({1\sp 2\sp 3\sp 4\sp 5\sp 6 \atop - 3\sp 6\sp 4\sp 2\sp 1\sp 5}\right)$$ -$$\pi_2\pi_1 = \left({1\sp 2\sp 3\sp 4\sp 5\sp 6 \atop - 3\sp 1\sp 4\sp 5\sp 6\sp 2}\right)$$ -$$\pi_3\pi_4 = \left({1\sp 2\sp 3\sp 4\sp 5\sp 6\sp 7\sp 8 \atop - 1\sp 3\sp 8\sp 5\sp 7\sp 4\sp 6\sp 2}\right)$$ -$$\pi_4\pi_3 = \left({1\sp 2\sp 3\sp 4\sp 5\sp 6\sp 7\sp 8 \atop - 5\sp 4\sp 3\sp 6\sp 7\sp 8\sp 1\sp 2}\right)$$ - -\bye -- cgit