1,443 research outputs found
On some intriguing problems in Hamiltonian graph theory -- A survey
We survey results and open problems in Hamiltonian graph theory centred around three themes: regular graphs, -tough graphs, and claw-free graphs
Polyhedra with few 3-cuts are hamiltonian
In 1956, Tutte showed that every planar 4-connected graph is hamiltonian. In
this article, we will generalize this result and prove that polyhedra with at
most three 3-cuts are hamiltonian. In 2002 Jackson and Yu have shown this
result for the subclass of triangulations. We also prove that polyhedra with at
most four 3-cuts have a hamiltonian path. It is well known that for each non-hamiltonian polyhedra with 3-cuts exist. We give computational
results on lower bounds on the order of a possible non-hamiltonian polyhedron
for the remaining open cases of polyhedra with four or five 3-cuts.Comment: 21 pages; changed titl
A Survey of Best Monotone Degree Conditions for Graph Properties
We survey sufficient degree conditions, for a variety of graph properties,
that are best possible in the same sense that Chvatal's well-known degree
condition for hamiltonicity is best possible.Comment: 25 page
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