query: How to demonstrate that there would exist a vertex with degree less than $ 5$?
positive_passages.docid: 27805
positive_passages.text: Every planar graph has a vertex of degree at most 5.
negative_passages.docid: 79091
negative_passages.text: Please guide me to draw this : graph of $x \geq 5$ and $y \geq 5$
negative_passages.docid: 54875
negative_passages.text: How to prove polynomials with degree $n$ does not form a vector space?
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: 6429
negative_passages.text: prove that a connected graph with $n$ vertices has at least $n-1$ edges
negative_passages.docid: 100466
negative_passages.text: The number of labelled graphs with all vertices of even degree
negative_passages.docid: 157487
negative_passages.text: Showing a polynomial having at least one integer root under certain conditions has precisely one integer root
negative_passages.docid: 94838
negative_passages.text: Show that a self-complementary graph contains an odd number of vertices with degree $(n-1)/2$
negative_passages.docid: 52261
negative_passages.text: Proof that any self-complementary graph has to have $4k$ or $4k+1$ vertex, for some $k \in \mathbb N$
negative_passages.docid: 120558
negative_passages.text: If $H$ has maximum vertex degree at most $3$ and is a minor of $G$, then $H$ is a topological minor of $G$.
negative_passages.docid: 121304
negative_passages.text: Is the set of polynomials of degree less than or equal to $n$ closed?
negative_passages.docid: 43300
negative_passages.text: The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$
negative_passages.docid: 157150
negative_passages.text: Is the maximum degree of a planar graph 5?
negative_passages.docid: 106914
negative_passages.text: Existence of Irreducible polynomials over $\mathbb{Z}$ of any given degree
negative_passages.docid: 60615
negative_passages.text: Product of $5$ consecutive integers cannot be perfect square
negative_passages.docid: 127277
negative_passages.text: Graph Theory: Tree has at least 2 vertices of degree 1
negative_passages.docid: 154303
negative_passages.text: Degree $1$ map from torus to sphere