query: When is a collection of integers $v_1, \ldots, v_k$ the degrees of the vertices of an undirected graph?
positive_passages.docid: 18383
positive_passages.text: List of ways to tell if degree sequence is impossible for a simple graph
negative_passages.docid: 17086
negative_passages.text: The number of (non-equal) forests on the vertex set V = {1, 2, ...,n} that contains exactly 2 connected components is given by
negative_passages.docid: 68172
negative_passages.text: Erdős-Straus conjecture
negative_passages.docid: 147282
negative_passages.text: Prove that in every graph with at least two vertices, there are at least two vertices which have the same degree?
negative_passages.docid: 83036
negative_passages.text: f(g(x)) has a degree divisible by n
negative_passages.docid: 117685
negative_passages.text: Prove that a bipartite planar graph has a vertex of degree at most 3
negative_passages.docid: 19219
negative_passages.text: On the invertibility of the adjacency matrix of a graph
negative_passages.docid: 17868
negative_passages.text: How to calculate the number of possible connected simple graphs with $n$ labelled vertices
negative_passages.docid: 99806
negative_passages.text: Given an undirected Graph
negative_passages.docid: 117349
negative_passages.text: counting triangles in a graph or its complement
negative_passages.docid: 91134
negative_passages.text: In any finite graph with at least two vertices, there must be two vertices with the same degree
negative_passages.docid: 126060
negative_passages.text: Proving that a Euler Circuit has a even degree for every vertex
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: 19413
negative_passages.text: Degree sequence multigraph without loop
negative_passages.docid: 36034
negative_passages.text: Degree of splitting field less than 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: 71990
negative_passages.text: Prove there always exists a partition such that vertices in each part have even degree