2) Hamilton cycles: A Hamilton cycle is a cycle which contains all the vertices of the graph.
3) Embeddings of graphs: This is a natural (but difficult) continuation of the previous question where the aim is to embed more general structures than Hamilton cycles - there has been exciting progress here in recent years which has opened up new avenues.
1] be a Hamilton cycle in <N(w)> and let X = G - N(w).
i]), there is a Hamilton cycle of <N(x)> that contains the edge [X.
Then, the Hamilton cycle for m can be obtained in this case as per the following figure (only above possible cases).
As an example, Figure 15 shows a hamilton cycle for m = 3, k = 8, l = 4.
Keywords: Knodel Graphs, Hamilton Cycle Decomposition, Tensor Product, Bieulerian Graph
We say that a k-regular graph G admits a Hamilton cycle decomposition, if the edge set of G can be partitioned into Hamilton cycles or Hamilton cycles together with a 1-factor according as k is even or odd, respectively.
A graph G is hamiltonian if it has a Hamilton cycle (a cycle containing all the vertices of G), and traceable if it has a Hamilton path (a path containing all the vertices of G).
If v and w are nonadjacent vertices in V(G - S), then (G - S) + vw has a Hamilton cycle containing [y.
One of the classical problems of graph theory is the study of sufficient conditions for a graph to contain a Hamilton cycle
Fink, Perfect matchings extend to Hamilton cycles
in hypercubes, J.