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Date: 11-5-2022
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The size of a minimum edge cover in a graph is known as the edge cover number of , denoted .
If a graph has no isolated points, then
where is the matching number and is the vertex count of (Gallai 1959, West 2000).
Gallai, T. "Über extreme Punkt- und Kantenmengen." Ann. Univ. Sci. Budapest, Eőtvős Sect. Math. 2, 133-138, 1959.
West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2000.
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