List questions from matching-theory

Published on 06 Jul 2020 - 17:09

927

Views

Given a perfect fractional matching, does there exist a perfect matching with heavy edges?

Published on 08 Jul 2020 - 21:02

284

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$k$ regular graph with $(k+1)^2 -1$ vertices and matching saturates $n-k$ vertices

Published on 12 Jul 2020 - 7:36

1k

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Can you win the monochromatic urn game?

Published on 13 Jul 2020 - 9:49

1.6k

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Proving a graph doesn't have a perfect matching

Published on 19 Jul 2020 - 10:07

913

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A tree has at most one perfect matching (proof verification)

Published on 20 Jul 2020 - 20:50

51

Views

Low-computation algorithm for near-optimally assigning N options to N users given 1-N ranked list of options per user.

Published on 25 Mar 2026 - 10:26

381

Views

Consider $G$ is a connected graph. For any vertex $v$ in $G$, prove that there exists a matching for which $v$ is saturated.

Published on 27 Jul 2020 - 19:54

53

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Is it possible to match two women to each man so that every women will not match more than once

Published on 28 Jul 2020 - 17:28

446

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Matching, augmenting path Lemma

Published on 25 Oct 2016 - 0:12

2.6k

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Matching in a bipartite graph saturating $X$

Published on 13 Nov 2016 - 12:47

298

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Proof bipartite graph matching

Published on 14 Nov 2016 - 0:35

1k

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Matching in a bipartite graph that saturates all vertices

Published on 26 Nov 2016 - 16:05

588

Views

Is there a mistake in this proof of Hall's theorem?

Published on 27 Nov 2016 - 4:19

1.3k

Views

$2$-edge-connected graph has perfect matching

Published on 15 Dec 2016 - 20:43

List Question

Matchings in bipartite graph

Given a perfect fractional matching, does there exist a perfect matching with heavy edges?

$k$ regular graph with $(k+1)^2 -1$ vertices and matching saturates $n-k$ vertices

Can you win the monochromatic urn game?

Proving a graph doesn't have a perfect matching

A tree has at most one perfect matching (proof verification)

Low-computation algorithm for near-optimally assigning N options to N users given 1-N ranked list of options per user.

Consider $G$ is a connected graph. For any vertex $v$ in $G$, prove that there exists a matching for which $v$ is saturated.

Is it possible to match two women to each man so that every women will not match more than once

Matching, augmenting path Lemma

Matching in a bipartite graph saturating $X$

Proof bipartite graph matching

Matching in a bipartite graph that saturates all vertices

Is there a mistake in this proof of Hall's theorem?

$2$-edge-connected graph has perfect matching

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