Question

How many pair-wise touching "shapes" are there in an $n\times n\times n$ grid?

score 115 · Answer 1 · 2026-03-20 08:50:19

115

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How many pair-wise touching "shapes" are there in an $n\times n\times n$ grid?

Published on 20 Mar 2026 - 8:50

score 108 · Answer 2 · 2026-03-25 13:28:24

108

Views

number of edges in infinite graph

Published on 25 Mar 2026 - 13:28

score 177 · Answer 3 · 2026-03-25 03:00:38

177

Views

Splitting polygons with at most ${3n\over 4}$ vertices

Published on 25 Mar 2026 - 3:00

score 863 · Answer 4 · 2018-02-22 21:06:28

863

Views

Prove that if G is nearly strongly connected there exists vertex such that every vertex is reachable

Published on 22 Feb 2018 - 21:06

score 77 · Answer 5 · 2026-03-22 22:21:08

77

Views

Is there a dihedral graph in which the vertices have degree 4?

Published on 22 Mar 2026 - 22:21

score 59 · Answer 6 · 2026-03-26 02:57:49

59

Views

Proof that direct distance from $a$ to $b$ is at most the distance of any other path from $a$ to $b$

Published on 26 Mar 2026 - 2:57

score 233 · Answer 7 · 2026-03-17 07:05:48

233

Views

Number of independent vertex sets in a graph.

Published on 17 Mar 2026 - 7:05

score 144 · Answer 8 · 2026-03-22 22:48:32

144

Views

Finding Hamiltonian cycle for $N\times M$ grid where $N$ is even

Published on 22 Mar 2026 - 22:48

score 928 · Answer 9 · 2018-02-23 17:59:46

928

Views

What is tangled graph

Published on 23 Feb 2018 - 17:59

score 90 · Answer 10 · 2018-02-24 02:43:53

90

Views

Augmenting path of edge-disjoint paths

Published on 24 Feb 2018 - 2:43

score 487 · Answer 11 · 2026-03-25 23:15:56

487

Views

Petersen Graph - no $3$ node circles

Published on 25 Mar 2026 - 23:15

score 1.1k · Answer 12 · 2018-02-24 16:42:43

Prove or disprove that if $G$ and $H$ are two edge-disjoint graphs on the same vertex set $V$, then $\chi(G\cup H) \le \chi(G)+ \chi(H)$

score 1k · Answer 13 · 2026-03-22 22:53:24

1k

Views

Prove or disprove that every graph $G$ satisfies $\chi (G) \le |G| - \alpha (G) + 1$

Published on 22 Mar 2026 - 22:53

score 279 · Answer 14 · 2026-03-20 04:44:39

279

Views

$6$-regular graph of order $25$ and diameter $2$

Published on 20 Mar 2026 - 4:44

score 64 · Answer 15 · 2026-03-25 03:58:14

64

Views

Looking for a challenging task or variant related to the knight's tour problem

Published on 25 Mar 2026 - 3:58

List Question

How many pair-wise touching "shapes" are there in an $n\times n\times n$ grid?

number of edges in infinite graph

Splitting polygons with at most ${3n\over 4}$ vertices

Prove that if G is nearly strongly connected there exists vertex such that every vertex is reachable

Is there a dihedral graph in which the vertices have degree 4?

Proof that direct distance from $a$ to $b$ is at most the distance of any other path from $a$ to $b$

Number of independent vertex sets in a graph.

Finding Hamiltonian cycle for $N\times M$ grid where $N$ is even

What is tangled graph

Augmenting path of edge-disjoint paths

Petersen Graph - no $3$ node circles

Prove or disprove that if $G$ and $H$ are two edge-disjoint graphs on the same vertex set $V$, then $\chi(G\cup H) \le \chi(G)+ \chi(H)$

Prove or disprove that every graph $G$ satisfies $\chi (G) \le |G| - \alpha (G) + 1$

$6$-regular graph of order $25$ and diameter $2$

Looking for a challenging task or variant related to the knight's tour problem

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