Cubic graphs with large circumference deficit
نویسندگان
چکیده
The circumference c(G) of a graph G is the length of a longest cycle. By exploiting our recent results on resistance of snarks, we construct infinite classes of cyclically 4-, 5and 6-edge-connected cubic graphs with circumference ratio c(G)/|V (G)| bounded from above by 0.876, 0.960 and 0.990, respectively. In contrast, the dominating cycle conjecture implies that the circumference ratio of a cyclically 4-edgeconnected cubic graph is at least 0.75. In addition, we construct snarks with large girth and large circumference deficit, solving Problem 1 proposed in [J. Hägglund and K. Markström, On stable cycles and cycle double covers of graphs with large circumference, Disc. Math. 312 (2012), 2540–2544].
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عنوان ژورنال:
- Journal of Graph Theory
دوره 82 شماره
صفحات -
تاریخ انتشار 2016