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1995 On the intersections of longest cycles in a graph
Iain A. Stewart, Ben Thompson
Experiment. Math. 4(1): 41-48 (1995).


We confirm a conjecture, due to Grötschel, regarding the intersection vertices of two longest cycles in a graph. In particular, we show that if G is a graph of circumference at least $k+1$, where $k\in\{6,7\}$, and G has two longest cycles meeting in a set W of k vertices, then W is an articulation set. Grötschel had previously proved this result for $k\in\{3,4,5\}$ and shown that it fails for $k > 7$. As corollaries, we obtain results regarding the minimum lengths of longest cycles in certain vertex-transitive graphs. Our proofs are novel in that they make extensive use of a computer, although the programs themselves are straightforward


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Iain A. Stewart. Ben Thompson. "On the intersections of longest cycles in a graph." Experiment. Math. 4 (1) 41 - 48, 1995.


Published: 1995
First available in Project Euclid: 3 September 2003

zbMATH: 0841.05056
MathSciNet: MR1359416

Primary: 05C38

Rights: Copyright © 1995 A K Peters, Ltd.


Vol.4 • No. 1 • 1995
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