05A19-KonigEgervaryTheorem.tex

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\pmtitle{K\"onig-Egervary theorem}
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The {\em K\"onig-Egervary theorem} states that in a finite matrix of 0's and 1's, the maximum numbers of 1's such that no two are in a line, equals the minimum number of lines which collectively contain all the 1's. Here line means row or column.

Take this matrix, for example,

$$\begin{bmatrix}
1 & 0 & 0 & 0 & 0 & 1 \\
1 & 0 & 0 & 0 & 0 & 1 \\
0 & 1 & 0 & 0 & 0 & 1 \\
0 & 1 & 0 & 0 & 0 & 1 \\
1 & 0 & 1 & 1 & 1 & 0 \\
\end{bmatrix}$$

Here the max and min numbers (always equal) are 4.

\begin{thebibliography}{1}
\bibitem{ac} A. Chandra Babu, P. V. Ramakrishnan, ``New Proofs of Konig-Egervary Theorem And Maximal Flow-Minimal Cut Capacity Theorem Using O. R. Techniques'' {\it Indian J. Pure 
Appl. Math.} {\bf 22}(11) (1991): 905 - 911
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