query: Given a graph $G$ with $n$ vertices and $k$ connected components, show that the maximum number of edges is ${n - k + 1 \choose 2} $
positive_passages.docid: 28877
positive_passages.text: Graph with $k$ components.
negative_passages.docid: 93304
negative_passages.text: How to prove Graph with $n$ vertices has Edge Chromatic Number no more than $n/2$ edges
negative_passages.docid: 127965
negative_passages.text: Graph theory (Graph Connectivity)
negative_passages.docid: 59831
negative_passages.text: How to relate combinatorial proof to bipartite graphs?
negative_passages.docid: 71154
negative_passages.text: Why a complete graph has $\frac{n(n-1)}{2}$ edges?
negative_passages.docid: 73345
negative_passages.text: maximum size of a $k$-intersecting family of $[n]$
negative_passages.docid: 70761
negative_passages.text: Number of ways to connect sets of $k$ dots in a perfect $n$-gon
negative_passages.docid: 99806
negative_passages.text: Given an undirected Graph
negative_passages.docid: 101520
negative_passages.text: Let $G$ be a graph of minimum degree $k>1$. Show that $G$ has a cycle of length at least $k+1$
negative_passages.docid: 38466
negative_passages.text: Proving that the number of vertices of odd degree in any graph G is even
negative_passages.docid: 142917
negative_passages.text: Graph vertex chromatic number in a union of 2 sub-graphs
negative_passages.docid: 70282
negative_passages.text: Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
negative_passages.docid: 99746
negative_passages.text: Vertex cover in a graph with maximum degree of 3 and average degree of 2.
negative_passages.docid: 79730
negative_passages.text: $G$ is a planar, connected graph. Let $n$ be number of vertices, $m$ number of edges and $f$ number of faces. Prove that dual graph $G*$ has $f(G*)=n$
negative_passages.docid: 75101
negative_passages.text: Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
negative_passages.docid: 18117
negative_passages.text: Maximum number of edges in a simple graph?
negative_passages.docid: 113015
negative_passages.text: Eulerian Paths in a Complete Graph $K_5$