# Approximating the Circumference of 3-Connected Claw-free Graphs

Abstract (Summary)

Jackson and Wormald show that every 3-connected
K_1,d-free graph, on n vertices, contains a cycle of length at least 1/2 n^g(d) where g(d) = (log_2 6 + 2 log_2 (2d+1))^-1. For d = 3, g(d) ~ 0.122.
Improving this bound, we prove that if G is a 3-connected claw-free graph on at least 6 vertices, then there exists a cycle C in G such that |E(C)| is at least c n^g+5, where
g = log_3 2 and c > 1/7 is a constant.
To do this, we instead prove a stronger theorem that requires the cycle to contain two specified edges. We then use Tutte decomposition to partition the graph and then use the inductive
hypothesis of our theorem to find paths or cycles in the different parts of the decomposition.
Bibliographical Information:

Advisor:Duke, Richard; Yu, Xingxing; Vigoda, Eric; Thomas, Robin; Tetali, Prasad

School:Georgia Institute of Technology

School Location:USA - Georgia

Source Type:Master's Thesis

Keywords:mathematics

ISBN:

Date of Publication:08/25/2008