Subdivisions of graphs: A generalization of paths and cycles

One of the basic results in graph theory is Dirac's theorem, that every graph of order n 3 and minimum degree n/2 is Hamiltonian. This may be restated as: if a graph of order n and minimum degree n/2 contains a cycle C then it contains a spanning cycle, which is just a spanning subdivision of C. We show that the same conclusion is true if instead of C, we choose any graph H such that every connected component of H is non-trivial and contains at most one cycle. The degree bound can be improved to (n-t)/2 if H has t components that are trees. We attempt a similar generalization of the Corr

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Ch. Sobhan Babu, Ajit A. Diwan
• Keywords: Connected Component, DM 2008, Graph Theory, Minimum Degree