Unformatted text preview: (b) (5 points) Using the above recurrence, ﬁnd the number of matchings on the following graph: (c) (5 points) How could the above recurrence be modiﬁed to give the number of perfect matchings? 3. (10 points) Prove Hall’s Theorem by restricting Tutte’s 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 Menger’s 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
- Math, Bipartite graph, perfect matchings, bipartite, Menger’s Theorem