query: Prove that the line graph of a Hamiltonian simple graph is Hamiltonian.
positive_passages.docid: 20544
positive_passages.text: Proving that if $G$ has a Hamiltonian circuit, then the line graph $L(G)$ also has a Hamiltonian Circuit
negative_passages.docid: 27366
negative_passages.text: Prove that $g$ is tangent to the graph of $f$
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: 35458
negative_passages.text: Prove, that graph $G$ has at least $\chi(G)(\chi(G)-1)/2$ edges.
negative_passages.docid: 108508
negative_passages.text: Prove that every tournament contains at least one Hamiltonian path.
negative_passages.docid: 6429
negative_passages.text: prove that a connected graph with $n$ vertices has at least $n-1$ edges
negative_passages.docid: 55944
negative_passages.text: Chromatic polynomial of connected graph $ \leq x(x-1)^{n-1}$
negative_passages.docid: 131736
negative_passages.text: Proving a triangle with different edge colors exists in a graph.
negative_passages.docid: 140199
negative_passages.text: Proof that disjoint cycles commute
negative_passages.docid: 12060
negative_passages.text: Homeomorphism to graph
negative_passages.docid: 120065
negative_passages.text: Niven’s theorem proof.
negative_passages.docid: 48692
negative_passages.text: A problem about the graph theory
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: 43764
negative_passages.text: Prove $P_m X P_n$ is Hamiltonian if and only if at least one of $m,n$ is even
negative_passages.docid: 91253
negative_passages.text: Proving that every graph that each vertex at degree 2 must contain a cycle
negative_passages.docid: 41907
negative_passages.text: Triangulation of a simple polygon (elementary proof?)
negative_passages.docid: 148169
negative_passages.text: prove that line bisect section