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Prove that the complete bipartite graph $K_{3,s}$ has $s^23^{s-1}$ spanning trees for $s\geq2$

score 2.1k · Answer 1 · 2026-04-15 23:33:28

2.1k

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Prove that the complete bipartite graph $K_{3,s}$ has $s^23^{s-1}$ spanning trees for $s\geq2$

Published on 15 Apr 2026 - 23:33

score 160 · Answer 2 · 2026-04-17 10:05:04

160

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Algorithmic Graph Theory - perfect matching in bipartite graph when det(A) is not 0

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score 61 · Answer 3 · 2026-04-13 18:42:41

61

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How can I prove that this two statements are equivalent?

Published on 13 Apr 2026 - 18:42

score 640 · Answer 4 · 2026-04-17 15:20:47

640

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Published on 17 Apr 2026 - 15:20

score 542 · Answer 5 · 2026-04-17 03:44:39

542

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Prove that every simple graph $G$ contains a spanning subgraph, which is bipartite and $\deg(v') \geq \frac{1}{2}\deg(v)$.

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score 433 · Answer 6 · 2026-05-10 18:04:07

433

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score 82 · Answer 7 · 2026-04-14 14:59:32

82

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score 277 · Answer 8 · 2026-04-15 21:27:10

277

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score 644 · Answer 9 · 2026-04-17 16:01:51

644

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Prove that if G — (V, E) is an arbitrary bipartite graph, then $|E| \leq |V|^2/4$ using induction

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score 299 · Answer 10 · 2026-05-10 17:15:56

299

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Lower bound of number of independent sets

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score 109 · Answer 11 · 2026-04-15 11:17:25

109

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Why that a graphon is bipartite iff its odd cycle density is 0?

Published on 15 Apr 2026 - 11:17

score 333 · Answer 12 · 2026-04-13 23:16:54

333

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bipartite subgraph H

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score 237 · Answer 13 · 2026-04-14 01:24:48

237

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score 582 · Answer 14 · 2026-04-13 21:29:23

582

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score 263 · Answer 15 · 2026-05-10 20:52:25

263

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Finding a Hamiltonian Cycle from a perfect matching on a the bipartite graph

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List Question

Prove that the complete bipartite graph $K_{3,s}$ has $s^23^{s-1}$ spanning trees for $s\geq2$

Algorithmic Graph Theory - perfect matching in bipartite graph when det(A) is not 0

How can I prove that this two statements are equivalent?

Graph on $n$ vertices, each vertex of degree 3 or less. Can we color the vertices in a way such that...

Prove that every simple graph $G$ contains a spanning subgraph, which is bipartite and $\deg(v') \geq \frac{1}{2}\deg(v)$.

Graph which is Bipartite, has an Euler circuit, but not a Hamiltonian circuit

Help formulating a conjecture about the parity of every cycle length in a bipartite graph and proving it

graph theory problem - containing $K_{2,m}$

Prove that if G — (V, E) is an arbitrary bipartite graph, then $|E| \leq |V|^2/4$ using induction

Lower bound of number of independent sets

Why that a graphon is bipartite iff its odd cycle density is 0?

bipartite subgraph H

Bipartite Graph n-1 matchings

Bipartite graphs from permutations

Finding a Hamiltonian Cycle from a perfect matching on a the bipartite graph

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