126 research outputs found
Hamiltonian degree conditions which imply a graph is pancyclic
AbstractWe use a recent cycle structure theorem to prove that three well-known hamiltonian degree conditions (due to Chvátal, Fan, and Bondy) each imply that a graph is either pancyclic, bipartite, or a member of an easily identified family of exceptions
Hamiltonicity, independence number, and pancyclicity
A graph on n vertices is called pancyclic if it contains a cycle of length l
for all 3 \le l \le n. In 1972, Erdos proved that if G is a Hamiltonian graph
on n > 4k^4 vertices with independence number k, then G is pancyclic. He then
suggested that n = \Omega(k^2) should already be enough to guarantee
pancyclicity. Improving on his and some other later results, we prove that
there exists a constant c such that n > ck^{7/3} suffices
The Cycle Spectrum of Claw-free Hamiltonian Graphs
If is a claw-free hamiltonian graph of order and maximum degree
with , then has cycles of at least many different lengths.Comment: 9 page
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