Hamiltonicity, independence number, and pancyclicity
Copyright policy )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 = ��(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.
- UCLA United States
- University of California, Los Angeles United States
- UCLA United States
- UCLA United States
Eulerian and Hamiltonian graphs, Computational Theory and Mathematics, Hamilton cycle, FOS: Mathematics, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO), Paths and cycles, Theoretical Computer Science
Eulerian and Hamiltonian graphs, Computational Theory and Mathematics, Hamilton cycle, FOS: Mathematics, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO), Paths and cycles, Theoretical Computer Science
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