On pancyclism in hamiltonian graphs
نویسندگان
چکیده
We investigate the set of cycle lengths occurring in a hamiltonian graph with at least one or two vertices of large degree. We prove that in every case this set contains all the integers between 3 and some t, where t depends on the order of the graph and the degrees of vertices. c © 2002 Elsevier Science B.V. All rights reserved.
منابع مشابه
A Note on the Pancyclism of Block Intersection Graphs of Universal-Friend Friendship Hypergraphs
In this note, we consider the i-block intersection graphs (i-BIG) of a universal-friend friendship 3-hypergraph and show that they are pancyclic for i = 1, 2. We also show that the 1-BIG of a universalfriend friendship 3-hypergraph is Hamiltonian-connected.
متن کاملPancyclism and small cycles in graphs
We first show that if a graph G of order n contains a hamiltonian path connecting two nonadjacent vertices u and v such that d(u) + d(v) ≥ n, then G is pancyclic. By using this result, we prove that if G is hamiltonian with order n ≥ 20 and if G has two nonadjacent vertices u and v such that d(u) + d(v) ≥ n + z, where z = 0 when n is odd and z = 1 otherwise, then G contains a cycle of length m ...
متن کاملCycle-pancyclism in tournaments III
Let T be a hamiltonian tournament with n vertices and a hamiltonian cycle of T. For a cycle C k of length k in T we denote I (C k) = jA() \ A(C k)j, the number of arcs that and C k have in common. Let f(n; k; T;) = maxfI (C k)jC k Tg and f(n; k) = minff(n; k; T;)jT is a hamiltonian tournament with n vertices, and a hamiltonian cycle of Tg. In a previous paper 3] we studied the case of n 2k ? 4 ...
متن کاملGeometric-Arithmetic Index of Hamiltonian Fullerenes
A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.
متن کاملA conjecture on cycle-pancyclism in tournaments
Let T be a hamiltonian tournament with n vertices and γ a hamiltonian cycle of T . In previous works we introduced and studied the concept of cycle-pancyclism to capture the following question: What is the maximum intersection with γ of a cycle of length k? More precisely, for a cycle Ck of length k in T we denote Iγ(Ck) = |A(γ) ∩ A(Ck)|, the number of arcs that γ and Ck have in common. Let f(k...
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:
- Discrete Mathematics
دوره 251 شماره
صفحات -
تاریخ انتشار 2002