Approximating Longest Cycles in Graphs with Bounded Degrees

  title={Approximating Longest Cycles in Graphs with Bounded Degrees},
  author={Guantao Chen and Zhicheng Gao and Xingxing Yu and Wenan Zang},
  journal={SIAM J. Comput.},
Jackson and Wormald conjectured that if G is a 3-connected n-vertex graph with maximum degree d ≥ 4 then G has a cycle of length Ω(nd−1 ) and showed that the bound is best possible if true. In this paper we prove that this conjecture holds when d− 1 is replaced by max{64, 4d + 1}. Our proof implies a cubic algorithm for finding such a cycle. 

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 12 references

Finding a long cycle in a graph with a degree bound and a 3-cyclable minor

T. Feder, R. Motwani
View 5 Excerpts
Highly Influenced

Dividing a Graph into Triconnected Components

SIAM J. Comput. • 1973
View 4 Excerpts
Highly Influenced

Longest cycles in 3-connected graphs

Discrete Mathematics • 1997
View 2 Excerpts

On approximating the longest path in a graph, Algorithmica

D. Karger, R. Motwani, G.D.S. Ramkumar

Similar Papers

Loading similar papers…