Question

Extremal combinatorics problem on graph matching

score 78 · Answer 1 · 2026-05-05 05:35:18

78

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Extremal combinatorics problem on graph matching

Published on 05 May 2026 - 5:35

score 1.1k · Answer 2 · 2026-04-29 12:57:10

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 29 Apr 2026 - 12:57

score 601 · Answer 3 · 2026-04-29 12:55:29

601

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

Published on 29 Apr 2026 - 12:55

score 293 · Answer 4 · 2026-04-29 12:57:17

293

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Finding the maximum matching of the graph

Published on 29 Apr 2026 - 12:57

score 1.4k · Answer 5 · 2026-04-29 12:57:15

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 29 Apr 2026 - 12:57

score 178 · Answer 6 · 2026-04-15 07:00:28

178

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Minimum Matching Decomposition | proof verification

Published on 15 Apr 2026 - 7:00

score 54 · Answer 7 · 2026-04-29 12:57:17

54

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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 29 Apr 2026 - 12:57

score 189 · Answer 8 · 2026-04-16 14:32:43

189

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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 16 Apr 2026 - 14:32

score 638 · Answer 9 · 2026-04-29 12:57:38

638

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How to find the perfect matching?

Published on 29 Apr 2026 - 12:57

score 3.1k · Answer 10 · 2026-04-16 08:49:23

3.1k

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

Published on 16 Apr 2026 - 8:49

score 86 · Answer 11 · 2026-04-16 11:46:17

86

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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 16 Apr 2026 - 11:46

score 1.2k · Answer 12 · 2026-04-29 12:57:35

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 29 Apr 2026 - 12:57

score 194 · Answer 13 · 2026-04-16 19:46:55

194

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

Published on 16 Apr 2026 - 19:46

score 204 · Answer 14 · 2026-04-29 12:57:11

204

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

Published on 29 Apr 2026 - 12:57

score 260 · Answer 15 · 2026-04-15 21:43:18

260

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

Published on 15 Apr 2026 - 21:43

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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