An Asymptotic Version of the Multigraph 1-Factorization Conjecture
نویسندگان
چکیده
منابع مشابه
An asymptotic version of a conjecture by Enomoto and Ota
In 2000, Enomoto and Ota [2] stated the following conjecture: Conjecture 1 Let G be a graph of order n, and n 1 , n 2 , ..., n t be positive integers with t i=1 n i = n. If σ 2 (G) ≥ n + t − 1, then for any t distinct ver-The cases where t = 1, 2 follow from Theorems by Ore [4, 5]. Enomoto and Ota proved the conjecture for t = 3 and when almost all the n i are less than six. We prove the follow...
متن کاملNetwork Augmentation and the Multigraph Conjecture
Let Γ(n, m) denote the class of all graphs and multigraphs with n nodes and m edges. A central question in network reliability theory is the network augmentation problem: For G ∈ Γ(n, m) fixed, what H ∈ Γ(n, m + k) such that G ⊂ H is t-optimal, that is, maximizes the tree number t(H)? In the network synthesis problem, where G is the empty graph on n vertices, it is conjectured that all t-optima...
متن کاملAn oriented version of the 1-2-3 Conjecture
The well-known 1-2-3 Conjecture addressed by Karoński, Luczak and Thomason asks whether the edges of every undirected graph G with no isolated edge can be assigned weights from {1, 2, 3} so that the sum of incident weights at each vertex yields a proper vertex-colouring of G. In this work, we consider a similar problem for oriented graphs. We show that the arcs of every oriented graph − → G can...
متن کاملThe factorization of braided Hopf algebras and braided version of the 8th Kaplansky’s conjecture
We obtain the double factorization of braided bialgebras or braided Hopf algebras, give relation among integrals and semisimplicity of braided Hopf algebra and its factors. We find an example which show that the 8th Kaplansky’s conjecture does not hold for braided Hopf algebras.
متن کاملAn approximate version of Sidorenko’s conjecture
A beautiful conjecture of Erdős-Simonovits and Sidorenko states that if H is a bipartite graph, then the random graph with edge density p has in expectation asymptotically the minimum number of copies of H over all graphs of the same order and edge density. This conjecture also has an equivalent analytic form and has connections to a broad range of topics, such as matrix theory, Markov chains, ...
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: Journal of Graph Theory
سال: 2012
ISSN: 0364-9024
DOI: 10.1002/jgt.21629