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The edge covering number of the intersection of two matroids

✍ Scribed by Ron Aharoni; Eli Berger; Ran Ziv


Book ID
113567310
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
213 KB
Volume
312
Category
Article
ISSN
0012-365X

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Let G be the graph obtained as the edge intersection of two graphs G 1 , G 2 on the same vertex set V . We show that if at , where Ξ±() is the cardinality of the largest stable set. Moreover, for general G 1 and G 2 , we show that Ξ±(G) R(Ξ±(G 1 ) + 1, Ξ±(G 2 ) + 1) -1, where R(k, ) is the Ramsey numbe

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Let S be a nonempty finite set with cardinality m. Let M = (S, I(M)) be a matroid on S. Let x be an element of S which is not a loop of M. The covering number of x in M is the smallest positive integer s such that x is a coloop of the union of s copies of M. We investigate relations between the cove