Question

Given any $10$ people in a room, prove that among them there are either $3$ that know each other or $4$ that do not know each other.

score 271 · Answer 1 · 2026-03-29 03:36:44

271

Views

Given any $10$ people in a room, prove that among them there are either $3$ that know each other or $4$ that do not know each other.

Published on 29 Mar 2026 - 3:36

score 78 · Answer 2 · 2026-03-27 14:03:24

78

Views

Existence of a path of length $n/2$ in every bipartite graph with $d(A,B)=1/2$.

Published on 27 Mar 2026 - 14:03

score 514 · Answer 3 · 2021-10-13 21:33:20

514

Views

Given $2^{n-1}$ subsets of a set with $n$ elements with the property that any three have nonempty intersection, prove that ....

Published on 13 Oct 2021 - 21:33

score 83 · Answer 4 · 2026-03-27 15:20:02

83

Views

If the degree of every vertex in a graph on $n$ vertices is greater than $(1+ \sqrt{4n-3})/2$, then the graph contains a cycle of length $4$

Published on 27 Mar 2026 - 15:20

score 302 · Answer 5 · 2021-10-29 13:54:59

302

Views

Riordan numbers recurrence

Published on 29 Oct 2021 - 13:54

score 124 · Answer 6 · 2021-11-03 14:57:15

124

Views

Bollobás Modern Graph Theory upper bound for Zarankiewicz problem

Published on 03 Nov 2021 - 14:57

score 52 · Answer 7 · 2021-11-17 02:57:00

52

Views

Minimum number of intersections that must occur in any partition of a given size

Published on 17 Nov 2021 - 2:57

score 141 · Answer 8 · 2026-03-27 12:20:23

141

Views

What is $\operatorname{ex}(n, K_{2,3})$?

Published on 27 Mar 2026 - 12:20

score 255 · Answer 9 · 2021-11-22 05:21:09

255

Views

More elegant proofs of $\binom a2+\binom b2\leq \binom{a+b-1}2$

Published on 22 Nov 2021 - 5:21

score 28 · Answer 10 · 2021-11-29 04:42:49

28

Views

A set of $m$ vectors in $\mathbb{F}_3^n$ such that every subset of $n$ vectors is linearly independent?

Published on 29 Nov 2021 - 4:42

score 133 · Answer 11 · 2026-03-27 13:45:32

133

Views

Extremal combinatorics

Published on 27 Mar 2026 - 13:45

score 73 · Answer 12 · 2021-12-09 22:12:42

73

Views

Number of unique pairings of k values.

Published on 09 Dec 2021 - 22:12

score 320 · Answer 13 · 2026-03-26 07:52:44

320

Views

Family of sets with $|F_i| \equiv 2\pmod 3$ and $|F_i \cap F_j| \equiv 0 \pmod 3$

Published on 26 Mar 2026 - 7:52

score 65 · Answer 14 · 2022-01-01 15:55:05

65

Views

Minimum number of intersecting diagonals on a convex polygon

Published on 01 Jan 2022 - 15:55

score 237 · Answer 15 · 2022-01-06 11:22:26

237

Views

Number of subsets of the same size and pairwise intersecting in at most one point

Published on 06 Jan 2022 - 11:22

List Question

Given any $10$ people in a room, prove that among them there are either $3$ that know each other or $4$ that do not know each other.

Existence of a path of length $n/2$ in every bipartite graph with $d(A,B)=1/2$.

Given $2^{n-1}$ subsets of a set with $n$ elements with the property that any three have nonempty intersection, prove that ....

If the degree of every vertex in a graph on $n$ vertices is greater than $(1+ \sqrt{4n-3})/2$, then the graph contains a cycle of length $4$

Riordan numbers recurrence

Bollobás Modern Graph Theory upper bound for Zarankiewicz problem

Minimum number of intersections that must occur in any partition of a given size

What is $\operatorname{ex}(n, K_{2,3})$?

More elegant proofs of $\binom a2+\binom b2\leq \binom{a+b-1}2$

A set of $m$ vectors in $\mathbb{F}_3^n$ such that every subset of $n$ vectors is linearly independent?

Extremal combinatorics

Number of unique pairings of k values.

Family of sets with $|F_i| \equiv 2\pmod 3$ and $|F_i \cap F_j| \equiv 0 \pmod 3$

Minimum number of intersecting diagonals on a convex polygon

Number of subsets of the same size and pairwise intersecting in at most one point

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