A well-known conjecture of Thomassen states that every cycle of maximum order in a 33-connected graph contains a chord. While many partial results towards this conjecture have been obtained, the conjecture itself remains unsolved. In this paper, we prove a stronger result without a connectivity assumption for graphs of high minimum degree, which shows Thomassen's conjecture holds in that case. This result is within a constant factor of best possible. In the process of proving this, we prove a more general result showing that large minimum degree forces a large difference between the order of the largest cycle and the order of the largest chordless cycle.
|Journal||The Electronic Journal of Combinatorics|
|Number of pages||8|
|Publication status||Published - 2017|