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Unformatted text preview: (b) (5 points) Using the above recurrence, nd the number of matchings on the following graph: (c) (5 points) How could the above recurrence be modied to give the number of perfect matchings? 3. (10 points) Prove Halls Theorem by restricting Tuttes Theorem to the bipartite case and exhibiting that the Hall criterion follows from the Tutte criterion if G is bipartite. 4. (5 points) Show without using Mengers Theorem that if G is 2-connected and u and v are distinct vertices of G , there is a cycle in G containing both u and v . A man is about thirty-eight before he stockpiles enough socks to be able to get one matching pair. Merrily Harpur Page 1 of 1 Due February 4, 2010...
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- Spring '09