query: $G =(V,E)$ is $k$-connected ($k \geq 2$), prove that for every subset $S \subseteq V $, |S|=k there exists a cycle in $G$ that goes through all of $S$
positive_passages.docid: 94928
positive_passages.text: Every $k$ vertices in an $k$ - connected graph are contained in a cycle.
negative_passages.docid: 1453
negative_passages.text: Prove that the graph is connected
negative_passages.docid: 115695
negative_passages.text: If $X$ is a connected subset of a connected space $M$ then the complement of a component of $M \setminus X$ is connected
negative_passages.docid: 49465
negative_passages.text: How many Hamiltonian cycles are there in a complete graph $K_n$ ($n\geq 3$) Why?
negative_passages.docid: 35458
negative_passages.text: Prove, that graph $G$ has at least $\chi(G)(\chi(G)-1)/2$ edges.
negative_passages.docid: 109682
negative_passages.text: Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
negative_passages.docid: 123149
negative_passages.text: Prove that $E$ is disconnected iff there exists two open disjoint sets $A$,$B$ in $X$
negative_passages.docid: 104855
negative_passages.text: Prove that $N \subset Z(G)$
negative_passages.docid: 75101
negative_passages.text: Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
negative_passages.docid: 102084
negative_passages.text: How to show path-connectedness of $GL(n,\mathbb{C})$
negative_passages.docid: 65744
negative_passages.text: How can I Prove that H=G or K=G
negative_passages.docid: 62911
negative_passages.text: Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
negative_passages.docid: 130455
negative_passages.text: If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
negative_passages.docid: 116932
negative_passages.text: Proving a simple graph is a connected graph
negative_passages.docid: 23225
negative_passages.text: Union of connected subsets is connected if intersection is nonempty
negative_passages.docid: 93623
negative_passages.text: Showing that every connected open set in a locally path connected space is path connected
negative_passages.docid: 51145
negative_passages.text: Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?