A graph containing at least one Hamiltonian cycle is called Hamiltonian graph
. This optimization problem can be formally defined as follows:
Skupien, On the smallest non-Hamiltonian locally Hamiltonian graph, J.
Question 2 Is 14 the smallest order of a connected nontraceable locally hamiltonian graph?
We are particularly interested in the traceability properties of locally connected, locally traceable and locally hamiltonian graphs. We abbreviate locally connected to LC, locally traceable to LT and locally hamiltonian to LH.
Cardoso, "Necessary and sufficient conditions for a Hamiltonian graph
," Journal of Combinatorial Mathematics and Combinatorial Computing, vol.
For a graph G to be k-cyclic Hamiltonian, We call such an integer k as a cyclic hamiltonian generator of G, or G as cyclic hamiltonian graph
generated by k.
They cover fundamental concepts and basic results; graph isomorphisms, subgraphs, the complement of a graph, and graphic sequences; bipartite graphs and trees; Eulerian multigraphs and the Chinese postman problem; Hamiltonian graphs
and the traveling salesman problem; connectivity; independence, matching, and covering; vertex-colorings and planar graphs; domination; and digraphs and tournaments.
Chapters cover Cartesian products, more classical products such as Hamiltonian graphs
, invariants, Algebra and other topics.
are also explained, including those that are optimal k-fault tolerant and optimal 1- fault tolerant.
In other words, Theorem 5 further extends Ho's formulas for fault tolerant Hamiltonian graphs.
On the extremal number of edges in Hamiltonian graphs. J.
Early chapters present fundamentals of graph theory that lie outside of graph colorings, including basic terms and results, trees and connectivity, Eulerian and Hamiltonian graphs
, matching and factorizations, and graph embeddings.