List questions from matching-theory

Published on 14 Apr 2026 - 17:02

360

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Weaker version of Hall's condition

Published on 16 Apr 2026 - 8:45

146

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Matching of size at least $\frac{|E(G)|}{3}$ in the line graph $L(G)$ of a graph $G$

Published on 17 Apr 2026 - 9:36

700

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Number of Perfect Matching in Complete Graph - Proof Explanation

Published on 16 Apr 2026 - 14:07

104

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Proof of a Lemma for Saturated Non-Factorizable Graphs

Published on 13 Apr 2026 - 1:06

366

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Prove it is impossible for every male to be paired with their last choice in the stable marriage algorithm (male proposing)

Published on 10 May 2026 - 16:13

1.4k

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Identifying a Maximum matching and a minimum cover for a specific bipartite graph

Published on 15 Apr 2026 - 5:59

28

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How to set number of pairings in relation to cost

Published on 10 Apr 2026 - 21:24

99

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Prove that there exists a set $Y$ such that for every $v$, there exists $y \in Y$ that is incident to $v$.

Published on 13 Apr 2026 - 14:48

431

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Unique matching in a bipartite graph

Published on 13 Apr 2026 - 17:23

1.2k

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Perfect matchings in bipartite graphs.

Published on 17 Apr 2026 - 7:36

281

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Is the converse true?

Published on 30 Apr 2026 - 13:48

190

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Exercise 6.5 on p.133 in "Introduction to Graph Theory 5th Edition" by Robin J. Wilson.

Published on 16 Apr 2026 - 11:43

46

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Choice of augmenting path in the Augmenting Path Algorithm + Proof of correctness

Published on 11 Apr 2026 - 8:56

110

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What can we say about graph G?

Published on 15 Apr 2026 - 10:40

List Question

Perfect matching in random bipartite graph - with fixed probability

Weaker version of Hall's condition

Matching of size at least $\frac{|E(G)|}{3}$ in the line graph $L(G)$ of a graph $G$

Number of Perfect Matching in Complete Graph - Proof Explanation

Proof of a Lemma for Saturated Non-Factorizable Graphs

Prove it is impossible for every male to be paired with their last choice in the stable marriage algorithm (male proposing)

Identifying a Maximum matching and a minimum cover for a specific bipartite graph

How to set number of pairings in relation to cost

Prove that there exists a set $Y$ such that for every $v$, there exists $y \in Y$ that is incident to $v$.

Unique matching in a bipartite graph

Perfect matchings in bipartite graphs.

Is the converse true?

Exercise 6.5 on p.133 in "Introduction to Graph Theory 5th Edition" by Robin J. Wilson.

Choice of augmenting path in the Augmenting Path Algorithm + Proof of correctness

What can we say about graph G?

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