(a) Show that there are, up to isomorphism, exactly 8 matroids whose underlying set has three...

(a) Show that there are, up to isomorphism, exactly 8 matroids whose underlying set has three elements. Calling the elements a, b, c, exhibit, for each of these matroids, its bases, cycles and independent sets.

(b) Consider the matroid M on the set E = {a, b, c, d}, where the bases are the subsets of E having precisely two elements. Detrmine all the cycles of M, and show that there is no graph G such that M is the cycle matroid M(G).

Expert Solution

Colby Messinger answered 1 year ago

(a) Show that there are, up to isomorphism, exactly 8 matroids whose underlying set has three...

(a) Show that there are, up to isomorphism, exactly 8 matroids whose underlying set has three elements. Calling the elements a,b,c, exhibit, for each of these matroids, its bases, cycles and independent sets. (b) Consider the matroid M on the set E = {a,b,c,d}, where the bases are the subsets of E having precisely two elements. Detrmine all the cycles of M, and show that there is no graph G such that M is the cycle matroid M(G).

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An amusement park, whose customer set is made up of two markets, adults and children, has...

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Question

(a) Show that there are, up to isomorphism, exactly 8 matroids whose underlying set has three...

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