Avoiding 7-Circuits in 2-Factors of Cubic Graphs
نویسنده
چکیده
We show that every bridgeless cubic graph G on n vertices other than the Petersen graph has a 2-factor with at most 2(n−2)/15 circuits of length 5. An infinite family of graphs attains this bound. We also show that G has a 2-factor with at most n/5.83 odd circuits. This improves the previously known bound of n/5.41 [Lukoťka, Máčajová, Mazák, Škoviera: Small snarks with large oddness, arXiv:1212.3641 [cs.DM]].
منابع مشابه
Avoiding 5-circuits in a 2-factor of cubic graphs
We show that every bridgeless cubic graph G on n vertices other than the Petersen graph has a 2-factor with at most 2(n−2)/15 circuits of length 5. An infinite family of graphs attains this bound. We also show that G has a 2-factor with at most n/5.83 odd circuits. This improves the previously known bound of n/5.41 [Lukoťka, Máčajová, Mazák, Škoviera: Small snarks with large oddness, arXiv:1212...
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 29 شماره
صفحات -
تاریخ انتشار 2014