query: Why does a connected planar simple graph has a vertex of degree at most five?
positive_passages.docid: 157150
positive_passages.text: Is the maximum degree of a planar graph 5?
negative_passages.docid: 110422
negative_passages.text: Prove that a graph $G$ is a forest if and only if every induced subgraph of $G$ contain a vertex of degree at most $1$
negative_passages.docid: 125713
negative_passages.text: How to justify unicyclic connected graphs formula?
negative_passages.docid: 116494
negative_passages.text: What happens to the connectedness of $\mathbb R^2$ when countable many points are removed?
negative_passages.docid: 145718
negative_passages.text: Proving that A connected graph on $n$ vertices is a tree iff it has $n-1$ edges
negative_passages.docid: 142917
negative_passages.text: Graph vertex chromatic number in a union of 2 sub-graphs
negative_passages.docid: 39753
negative_passages.text: Proving that in a simple graph with $n$ vertices, two vertices have the same degree
negative_passages.docid: 65088
negative_passages.text: Why do you count a loop as a double in graph degree?
negative_passages.docid: 99931
negative_passages.text: Number of connected graphs on labeled vertices, counted according to parity
negative_passages.docid: 100168
negative_passages.text: Prove the existence of a graph of 15 vertices with some vertices degree given
negative_passages.docid: 129752
negative_passages.text: How to find whether it is possible for each vertex of a graph to have a different degree?
negative_passages.docid: 116932
negative_passages.text: Proving a simple graph is a connected graph
negative_passages.docid: 10910
negative_passages.text: How many edges does an undirected tree with $n$ nodes have?
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: 127277
negative_passages.text: Graph Theory: Tree has at least 2 vertices of degree 1
negative_passages.docid: 33316
negative_passages.text: Show that if $G$ is simple a graph with $n$ vertices and 􏰈the number of edges $m>\binom{n-1}{2}$, then $G$ is connected.
negative_passages.docid: 37754
negative_passages.text: Number of vertices of a complete graph with $n$ edges