Highly Influenced

# On the stability for pancyclicity

@article{Schiermeyer2001OnTS, title={On the stability for pancyclicity}, author={Ingo Schiermeyer}, journal={Discussiones Mathematicae Graph Theory}, year={2001}, volume={21}, pages={223-228} }

- Published in Discussiones Mathematicae Graph Theory 2001
DOI:10.7151/dmgt.1145

A property P defined on all graphs of order n is said to be k-stable if for any graph of order n that does not satisfy P , the fact that uv is not an edge of G and that G+uv satisfies P implies dG(u)+dG(v) < k. Every property is (2n−3)-stable and every k-stable property is (k+1)stable. We denote by s(P ) the smallest integer k such that P is k-stable and call it the stability of P . This number usually depends on n and is at most 2n−3. A graph of order n is said to be pancyclic if it contains… CONTINUE READING