Question

Extremal combinatorics problem on graph matching

score 71 · Answer 1 · 2026-03-17 14:31:07

71

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Extremal combinatorics problem on graph matching

Published on 17 Mar 2026 - 14:31

score 1.1k · Answer 2 · 2018-03-22 05:32:08

1.1k

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Prove that the $3$-regular graph, the triple flyswat, does not have a perfect matching but does have a matching with seven edges

Published on 22 Mar 2018 - 5:32

score 594 · Answer 3 · 2026-03-17 07:25:13

594

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Proof that bipartite graph has perfect matching if and only if zero sub-matrix is not included

Published on 17 Mar 2026 - 7:25

score 288 · Answer 4 · 2026-03-16 22:38:45

288

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Finding the maximum matching of the graph

Published on 16 Mar 2026 - 22:38

score 1.4k · Answer 5 · 2018-03-30 01:04:42

1.4k

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Proving that every connected graph of order 4 that is not $K_{1,3}$ has a perfect matching.

Published on 30 Mar 2018 - 1:04

score 175 · Answer 6 · 2026-03-17 09:20:29

175

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Minimum Matching Decomposition | proof verification

Published on 17 Mar 2026 - 9:20

score 50 · Answer 7 · 2018-04-20 17:20:46

50

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If $|M'| \gt 2 |M|$ then show that there is an edge $e' \in M'$ such that $|M| \cup \{e'\}$ is a matching in G.

Published on 20 Apr 2018 - 17:20

score 186 · Answer 8 · 2018-04-21 01:12:02

186

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Bipartite graph $G=(V,E)$ with parts $X$ and $Y$ satisfying $|\Gamma(S)| \geq \frac{|S|}{2}$ for any subset $S \subseteq X$

Published on 21 Apr 2018 - 1:12

score 632 · Answer 9 · 2026-03-16 21:36:56

632

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How to find the perfect matching?

Published on 16 Mar 2026 - 21:36

score 3.1k · Answer 10 · 2018-05-02 14:32:21

3.1k

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$G$ has a perfect matching if $G$ is bipartite and all vertices have the same degree

Published on 02 May 2018 - 14:32

score 83 · Answer 11 · 2018-05-03 18:36:12

83

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If $d_G(v)≤k \; \forall \; v \in V(G)$, then there exists a matching with $≥\frac{|V(G)|}{2k}$ edges

Published on 03 May 2018 - 18:36

score 1.2k · Answer 12 · 2018-05-04 12:28:35

1.2k

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Is it true that, for a tree, rank of adjacency matrix is equal to twice the matching number?

Published on 04 May 2018 - 12:28

score 189 · Answer 13 · 2018-05-06 00:17:08

189

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Can every partial transversal be extended to a maximum partial transversal?

Published on 06 May 2018 - 0:17

score 200 · Answer 14 · 2018-05-06 17:03:44

200

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How to apply Hall's Marriage Theorem given condition on vertex degrees

Published on 06 May 2018 - 17:03

score 257 · Answer 15 · 2026-03-17 17:19:51

257

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Number of matchings of a bipartite graph with $l$ edges

Published on 17 Mar 2026 - 17:19

List Question

Extremal combinatorics problem on graph matching

Prove that the $3$-regular graph, the triple flyswat, does not have a perfect matching but does have a matching with seven edges

Proof that bipartite graph has perfect matching if and only if zero sub-matrix is not included

Finding the maximum matching of the graph

Proving that every connected graph of order 4 that is not $K_{1,3}$ has a perfect matching.

Minimum Matching Decomposition | proof verification

If $|M'| \gt 2 |M|$ then show that there is an edge $e' \in M'$ such that $|M| \cup \{e'\}$ is a matching in G.

Bipartite graph $G=(V,E)$ with parts $X$ and $Y$ satisfying $|\Gamma(S)| \geq \frac{|S|}{2}$ for any subset $S \subseteq X$

How to find the perfect matching?

$G$ has a perfect matching if $G$ is bipartite and all vertices have the same degree

If $d_G(v)≤k \; \forall \; v \in V(G)$, then there exists a matching with $≥\frac{|V(G)|}{2k}$ edges

Is it true that, for a tree, rank of adjacency matrix is equal to twice the matching number?

Can every partial transversal be extended to a maximum partial transversal?

How to apply Hall's Marriage Theorem given condition on vertex degrees

Number of matchings of a bipartite graph with $l$ edges

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