منابع مشابه
Hamilton Cycles in Cubic Graphs
A graph is cubic if each of its vertex is of degree 3 and it is hamiltonian if it contains a cycle passing through all its vertices. It is known that if a cubic graph is hamiltonian, then it has at least three Hamilton cycles. This paper is about those works done concerning the number of Hamilton cycles in cubic graphs and related problems.
متن کاملChords of Longest Cycles in Cubic Graphs
We describe a general sufficient condition for a Hamiltonian graph to contain another Hamiltonian cycle. We apply it to prove that every longest cycle in a 3-connected cubic graph has a chord. We also verify special cases of an old conjecture of Sheehan on Hamiltonian cycles in 4-regular graphs and a recent conjecture on a second Hamiltonian cycle by Triesch, Nolles, and Vygen. 1997 Academic Press
متن کاملOn Hamilton cycles in cubic (m, n)-metacirculant graphs
Connected cubic (m,n)-metacircu1ant graphs, other than the Petersen , have been to be hamiltonian for m m divisible by 4 and m = 2. In this paper we two sufficient conditions tor connected cubic-metac1rcu1ant with m even, than 2 and not divisible by 4 to be hamiltonian. As corQ1laries, we show that every connected cubic-metacircu1ant other than the Petersen ,has a Hamilton if anyone of the cond...
متن کاملOn the Number of Cycles in 3-Connected Cubic Graphs
Let f(n) be the minimum number of cycles present in a 3-connected cubic graph on n vertices. In 1986, Barefoot, Clark and Entringer showed that f(n) is sub-exponential and conjectured that f(n) is super-polynomial. We verify this by showing that, for n su ciently large, 2 0:17 < f(n) < 2 0:95 : AMS Classi cation: 05C38 * Research supported in part by the Discrete Mathematics Grant of the Danish...
متن کاملNote on Petrie and Hamiltonian cycles in cubic polyhedral graphs
In this note we show that deciding the existence of a Hamiltonian cycle in a cubic plane graph is equivalent to the problem of the existence of an associated cubic plane multi-3-gonal graph with a Hamiltonian cycle which takes alternately left and right edges at each successive vertex, i.e. it is also a Petrie cycle. The Petrie Hamiltonian cycle in an n-vertex plane cubic graph can be recognize...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2017
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1926