query: undirected graphs and Hamiltonian cycles
positive_passages.docid: 145818
positive_passages.text: Edges on an even number of Hamilton cycles
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: 126060
negative_passages.text: Proving that a Euler Circuit has a even degree for every vertex
negative_passages.docid: 155090
negative_passages.text: A graph whose every odd cycle is a triangle is 4-colorable
negative_passages.docid: 58587
negative_passages.text: 3-regular graphs with no bridges
negative_passages.docid: 83872
negative_passages.text: Isomorphisms for graphs with loops and multiple edges
negative_passages.docid: 44563
negative_passages.text: Weakly Connected Graphs
negative_passages.docid: 63379
negative_passages.text: Enumerate non-isomorphic graphs on n vertices
negative_passages.docid: 108417
negative_passages.text: Cycles of length k in a complete simple graph with n vertices
negative_passages.docid: 100289
negative_passages.text: Question about self-complementary graphs
negative_passages.docid: 90747
negative_passages.text: Upper bound on $\chi(G)$ for a triangle-free graph
negative_passages.docid: 79180
negative_passages.text: When can an autonomous system be written using a Hamiltonian?
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: 113015
negative_passages.text: Eulerian Paths in a Complete Graph $K_5$
negative_passages.docid: 123567
negative_passages.text: Number of permutations which are products of exactly two disjoint cycles.
negative_passages.docid: 42513
negative_passages.text: Graph with Cycle and Two-Colorable
negative_passages.docid: 17268
negative_passages.text: Cycles in permutations of a given size