Question

Show that a 3-uniform hypergraph on $n \geq 5$ points, in which each pair of points occurs in the same (positive) number of edges, is not 2-colorable.

score 108 · Answer 1 · 2026-03-26 04:35:11

108

Views

Show that a 3-uniform hypergraph on $n \geq 5$ points, in which each pair of points occurs in the same (positive) number of edges, is not 2-colorable.

Published on 26 Mar 2026 - 4:35

score 67 · Answer 2 · 2026-03-25 14:25:27

67

Views

Parameter $d$ that makes the probability of the graph $G(n,\frac{d}{n})$ being $k$-colorable tends to $0$, as $n \to \infty$ , for $k \leq 2$.

Published on 25 Mar 2026 - 14:25

score 67 · Answer 3 · 2026-03-26 04:34:54

67

Views

Show that, if girth$(G) \geq g, \text{and } \delta(G) \geq d$, then $|V(G)|= n = \Omega(d^k), \text{where } k = \lfloor \frac{g-1}{2} \rfloor$.

Published on 26 Mar 2026 - 4:34

score 243 · Answer 4 · 2020-02-29 20:36:50

243

Views

what is the maximum number of vertices in a regular graph with fixed diameter

Published on 29 Feb 2020 - 20:36

score 109 · Answer 5 · 2026-03-26 04:31:39

109

Views

Simplification of the $\epsilon$-regularity condition in graphs.

Published on 26 Mar 2026 - 4:31

score 317 · Answer 6 · 2026-03-26 04:37:57

317

Views

If each edge of a graph $G=(V,E)$ belongs to exactly one triangle then $|E|=\omicron(n^{2})$.

Published on 26 Mar 2026 - 4:37

score 934 · Answer 7 · 2020-03-09 19:27:37

934

Views

Lower bound for number of triangles in simple graph.- very hard exercise

Published on 09 Mar 2020 - 19:27

score 123 · Answer 8 · 2020-03-11 16:09:36

123

Views

Edges on $K_{2,m}$ free graph

Published on 11 Mar 2020 - 16:09

score 317 · Answer 9 · 2020-04-28 18:33:53

317

Views

Extremal graph theory problems

Published on 28 Apr 2020 - 18:33

score 57 · Answer 10 · 2020-05-05 01:22:39

57

Views

Show ex$(n, H)\leq \left\lfloor\frac{n^2+n}{4}\right\rfloor$

Published on 05 May 2020 - 1:22

score 47 · Answer 11 · 2026-03-25 19:10:12

47

Views

In a random graph $G(n,p)$ with $\delta(G) \geq \delta$, how is the event $\{S \subset V \text{ is not a dominating set} \}$ characterized?

Published on 25 Mar 2026 - 19:10

score 188 · Answer 12 · 2026-03-25 23:38:44

188

Views

Cardinality of the Minimum Feedback Vertex Set of a directed graph

Published on 25 Mar 2026 - 23:38

score 302 · Answer 13 · 2020-06-16 06:41:48

302

Views

Largest Independent Sets in Triangle Free Graphs

Published on 16 Jun 2020 - 6:41

score 491 · Answer 14 · 2026-03-25 19:07:20

491

Views

Maximum number of edges of a bipartite connected graph with vertex classes of size $n$ and with no perfect matching

Published on 25 Mar 2026 - 19:07

score 400 · Answer 15 · 2020-06-20 01:19:54

400

Views

Show that the size of the Turan graph $T_r(n)$ is at least $(1 - \frac{1}{r}) \binom{n}{2}$.

Published on 20 Jun 2020 - 1:19

List Question

Show that a 3-uniform hypergraph on $n \geq 5$ points, in which each pair of points occurs in the same (positive) number of edges, is not 2-colorable.

Parameter $d$ that makes the probability of the graph $G(n,\frac{d}{n})$ being $k$-colorable tends to $0$, as $n \to \infty$ , for $k \leq 2$.

Show that, if girth$(G) \geq g, \text{and } \delta(G) \geq d$, then $|V(G)|= n = \Omega(d^k), \text{where } k = \lfloor \frac{g-1}{2} \rfloor$.

what is the maximum number of vertices in a regular graph with fixed diameter

Simplification of the $\epsilon$-regularity condition in graphs.

If each edge of a graph $G=(V,E)$ belongs to exactly one triangle then $|E|=\omicron(n^{2})$.

Lower bound for number of triangles in simple graph.- very hard exercise

Edges on $K_{2,m}$ free graph

Extremal graph theory problems

Show ex$(n, H)\leq \left\lfloor\frac{n^2+n}{4}\right\rfloor$

In a random graph $G(n,p)$ with $\delta(G) \geq \delta$, how is the event $\{S \subset V \text{ is not a dominating set} \}$ characterized?

Cardinality of the Minimum Feedback Vertex Set of a directed graph

Largest Independent Sets in Triangle Free Graphs

Maximum number of edges of a bipartite connected graph with vertex classes of size $n$ and with no perfect matching

Show that the size of the Turan graph $T_r(n)$ is at least $(1 - \frac{1}{r}) \binom{n}{2}$.

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