# Difference between revisions of "TU Wien:Diskrete Mathematik für Informatik VU (Gittenberger)/Übungstest 2019-11-08"

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1) Find three equivalent but different statements to "T is a tree". Choose two of them and prove their equivalence. | 1) Find three equivalent but different statements to "T is a tree". Choose two of them and prove their equivalence. | ||

+ | |||

2) Apply the matrix-tree theorem to find the number of spanning forests in a graph with two components. | 2) Apply the matrix-tree theorem to find the number of spanning forests in a graph with two components. | ||

− | 3) Is {{a, b, c}, { | + | |

+ | 3) Is {{a, b, c}, {{}, {a}, {b}, {c}, {a, b}, {a, c}}} an independence system? Is it even a matroid? |

## Revision as of 10:19, 9 November 2019

1) Find three equivalent but different statements to "T is a tree". Choose two of them and prove their equivalence.

2) Apply the matrix-tree theorem to find the number of spanning forests in a graph with two components.

3) Is {{a, b, c}, {{}, {a}, {b}, {c}, {a, b}, {a, c}}} an independence system? Is it even a matroid?