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    Approximating the circumference of 3-connected claw-free graphs

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    Date
    2008-08-25
    Author
    Bilinski, Mark
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    Abstract
    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.
    URI
    http://hdl.handle.net/1853/26516
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    • Georgia Tech Theses and Dissertations [22401]
    • School of Mathematics Theses and Dissertations [399]

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