Graphs with every k-matching in a Hamiltonian cycle
نویسندگان
چکیده
منابع مشابه
Bipartite graphs with every matching in a cycle
We give sufficient Ore-type conditions for a balanced bipartite graph to contain every matching in a hamiltonian cycle or a cycle not necessarily hamiltonian. Moreover, for the hamiltonian case we prove that the condition is almost best possible. © 2006 Elsevier B.V. All rights reserved.
متن کاملA degree condition implying that every matching is contained in a hamiltonian cycle
We give a degree sum condition for three independent vertices under which every matching of a graph lies in a hamiltonian cycle. We can show that the bound for the degree sum is almost best possible. Résumé Nous obtenons une condition portant sur la somme des degrés de trois sommets indépendants pour que tout couplage d’un graphe soit contenu dans un cycle hamiltonien. Nous prouvons que la born...
متن کاملk-ordered Hamiltonian graphs
A hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v1, v2, . . . , vk of k distinct vertices of G, there exists a hamiltonian cycle that encounters v1, v2, . . . , vk in this order. Theorems by Dirac and Ore, presenting sufficient conditions for a graph to be hamiltonian, are generalized to k-ordered hamiltonian graphs. The existence of k-ordered graphs with small m...
متن کاملEnumerating labeled graphs with a k-cycle
Cayley’s Tree Formula for enumerating labeled trees is well known. In this paper a more general result is presented for graphs with exactly one k-cycle (i.e. cycle on k vertices ).It is proved that for all integers n and k such that (n ≥ k ≥ 3), the number of possible labeled graphs on n vertices that contain exactly one k-cycle is ( n−1 k−1 ) nn−k. 1 ar X iv :0 90 9. 24 00 v1 [ m at h. C O ] 1...
متن کاملCycle spectra of Hamiltonian graphs
We prove that every Hamiltonian graph with n vertices and m edges has cycles of at least √ 4 7(m − n) different lengths. The coefficient 4/7 cannot be increased above 1, since when m = n2/4 there are √ m − n + 1 cycle lengths in Kn/2,n/2. For general m and n there are examples having at most 2 ⌈
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00174-0