A [k, k+1]-Factor Containing A Given Hamiltonian Cycle
نویسندگان
چکیده
We prove the following best possible result. Let k ≥ 2 be an integer and G be a graph of order n with minimum degree at least k. Assume n ≥ 8k− 16 for even n and n ≥ 6k−13 for odd n. If the degree sum of each pair of nonadjacent vertices of G is at least n, then for any given Hamiltonian cycle C of G, G has a [k, k + 1]-factor containing C. Submitted: December 15, 1997; Accepted: November 27, 1998. MR Subject Number: 05C75
منابع مشابه
Degree conditions for the existence of [k, k+1]-factors containing a given Hamiltonian cycle
Let k ≥ 2 be an integer and G a 2-connected graph of order |G| ≥ 3 with minimum degree at least k. Suppose that |G| ≥ 8k − 16 for even |G| and |G| ≥ 6k − 13 for odd |G|. We prove that G has a [k, k + 1]-factor containing a given Hamiltonian cycle if max{degG(x), degG(y)} ≥ |G|/2 for each pair of nonadjacent vertices x and y in G. This is best possible in the sense that there exists a graph havi...
متن کاملHamiltonian paths and cycles in hypertournaments
Given two integers n and k, n ≥ k > 1, a k-hypertournament T on n vertices is a pair (V, A), where V is a set of vertices, |V | = n and A is a set of k-tuples of vertices, called arcs, so that for any k-subset S of V , A contains exactly one of the k! k-tuples whose entries belong to S. A 2-hypertournament is merely an (ordinary) tournament. A path is a sequence v1a1v2a2v3...vt−1at−1vt of disti...
متن کاملThe Generalization of Dirac's Theorem for Hypergraphs
A substantial amount of research in graph theory continues to concentrate on the existence of hamiltonian cycles and perfect matchings. A classic theorem of Dirac states that a sufficient condition for an n-vertex graph to be hamiltonian, and thus, for n even, to have a perfect matching, is that the minimum degree is at least n/2. Moreover, there are obvious counterexamples showing that this is...
متن کاملAn Optimal XP Algorithm for Hamiltonian Cycle on Graphs of Bounded Clique-Width
For MSO2-expressible problems like Edge Dominating Set or Hamiltonian Cycle, it was open for a long time whether there is an algorithm which given a clique-width k-expression of an n-vertex graph runs in time f(k) · nO(1) for some function f . Recently, Fomin et al. (SIAM. J. Computing, 2014) presented several lower bounds; for instance, there are no f(k) · n-time algorithms for Edge Dominating...
متن کاملPancyclic graphs and linear forests
Given integers k, s, t with 0 ≤ s ≤ t and k ≥ 0, a (k, t, s)-linear forest F is a graph that is the vertex disjoint union of t paths with a total of k edges and with s of the paths being single vertices. If the number of single vertex paths is not critical, the forest F will simply be called a (k, t)-linear forest. A graph G of order n ≥ k + t is (k, t)-hamiltonian if for any (k, t)-linear fore...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 6 شماره
صفحات -
تاریخ انتشار 1999