Anki Deck Changes

Commit: 08e28d5a - add ln cards

Author: obrhubr <obrhubr@gmail.com>

Date: 2026-01-25T18:12:44+01:00

Changes: 5 note(s) changed (5 added, 0 modified, 0 deleted)

Note 1: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Classic
GUID: c1d=kD*#nb
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ETH::1._Semester::A&D::07._Graphs::1._Introduction_to_Graphs::1._Handshake_Lemma
How do we prove/disprove such as statement "There exists at least one undirected graph with 7 vertices in which all vertices have degree 3."

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ETH::1._Semester::A&D::07._Graphs::1._Introduction_to_Graphs::1._Handshake_Lemma
How do we prove/disprove such as statement "There exists at least one undirected graph with 7 vertices in which all vertices have degree 3."
We use the handshake Lemma: \(\sum \deg(v) = 7 \cdot 3 = 2 |E|\) but 21 is not even. Thus this cannot be true.
Field-by-field Comparison
Field Before After
Front How do we prove/disprove such as statement "There exists at least one undirected graph with 7 vertices in which all vertices have degree 3."
Back We use the handshake Lemma:&nbsp;\(\sum \deg(v) = 7 \cdot 3 = 2 |E|\)&nbsp;but 21 is not even. Thus this cannot be true.
Tags: ETH::1._Semester::A&D::07._Graphs::1._Introduction_to_Graphs::1._Handshake_Lemma

Note 2: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Cloze
GUID: kCvO2]PU.a
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ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation
 \(\ln(1)= 0\).

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ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation
 \(\ln(1)= 0\).
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Text &nbsp;\(\ln(1)= {{c1:: 0}}\).
Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation

Note 3: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Cloze
GUID: l`x
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ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation
\(\ln(2) - 1 < 0\)

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ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation
\(\ln(2) - 1 < 0\)
We have \(\ln(2) \sim 0.67\) thus it's negative.
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Field Before After
Text \(\ln(2) - 1 {{c1::&lt; :: relation}} 0\)
Extra We have&nbsp;\(\ln(2) \sim 0.67\)&nbsp;thus it's negative.
Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation

Note 4: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Classic
GUID: oIH*tMNYzG
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ETH::1._Semester::A&D::07._Graphs::1._Introduction_to_Graphs
Number of Edges in a Hamiltonian Path

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ETH::1._Semester::A&D::07._Graphs::1._Introduction_to_Graphs
Number of Edges in a Hamiltonian Path
Any hamiltonian path has exactly \(n - 1\) edges, as it visits every vertex once.
Field-by-field Comparison
Field Before After
Front Number of Edges in a Hamiltonian Path
Back Any hamiltonian path has exactly&nbsp;\(n - 1\)&nbsp;edges, as it visits every vertex once.
Tags: ETH::1._Semester::A&D::07._Graphs::1._Introduction_to_Graphs

Note 5: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Classic
GUID: r?O)Apht$a
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ETH::1._Semester::A&D::11._Minimum_Spanning_Trees
What's the runtime of any MST algorithm in a connected graph?

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ETH::1._Semester::A&D::11._Minimum_Spanning_Trees
What's the runtime of any MST algorithm in a connected graph?
The runtime is \(O(|E| \log |V|)\).
Field-by-field Comparison
Field Before After
Front What's the runtime of any MST algorithm in a connected graph?
Back The runtime is&nbsp;\(O(|E| \log |V|)\).
Tags: ETH::1._Semester::A&D::11._Minimum_Spanning_Trees
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