### Answers (127)

 7 Can an undirected graph be disconnected? 4 If a graph has a chromatic number $k$, then for any color there is a vertex of that color that has as neighbors all the other colors 3 How many $n$-digit sequences of $0,1 \ \text{or} \ 2$s contain an odd numbers of $0$s? 3 Question on graph theory regarding roads connecting a pair of cities 3 Group Theory Sylow Subgroup

### Reputation (2,246)

 +5 Show $\sum_{i \in V(G)}(out(i)-in(i))^3 \geq 0$ for a complete directed graph G with more than 3 vertices +5 Find a basis for witch the matrix consists only of 0 and 1 +8 Question regarding the connectedness of spanning 2-regular subgraphs +5 A probability question on using normal distriution

### Questions (74)

 26 Prove that there exists a triangle which can be cut into 2005 congruent triangles. 5 Determine all functions $f : \mathbb{N} \rightarrow \mathbb{N}$ such that, for every positive integer $n$, we have: $2n+2001≤f(f(n))+f(n)≤2n+2002$. 4 Different methods to calculate the limit of $\frac{a_nb_0+…+a_0b_n}{n}$ 3 limit of $a_n^{b_n}$ 3 Show the terms of a sequence $u_n$ is $0$.

### Tags (102)

 35 graph-theory × 56 9 coloring × 7 23 group-theory × 35 8 linear-algebra × 15 16 abstract-algebra × 25 8 directed-graphs × 2 11 combinatorics × 21 8 connectedness × 2 9 discrete-mathematics × 23 5 probability × 6

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