Edge-disjoint spanning trees and eigenvalues
نویسندگان
چکیده
منابع مشابه
Edge-disjoint spanning trees and eigenvalues
Article history: Received 17 July 2013 Accepted 25 November 2013 Available online 13 December 2013 Submitted by R. Brualdi MSC: 05C50 15A18 15A42
متن کاملEdge-Disjoint Spanning Trees, Edge Connectivity, and Eigenvalues in Graphs
Let λ2(G) and τ (G) denote the second largest eigenvalue and the maximum number of edge-disjoint spanning trees of a graph G, respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of τ (G), Cioabă and Wong conjectured that for any integers d , k ≥ 2 and a d -regular graph G, if λ2(G) < d − 2k−1 d+1 , then τ (G) ≥ k. They proved the conj...
متن کاملNote on edge-disjoint spanning trees and eigenvalues
Article history: Received 8 December 2013 Accepted 31 May 2014 Available online xxxx Submitted by R. Brualdi MSC: 05C50 15A18 15A42
متن کاملEdge-disjoint spanning trees and eigenvalues of regular graphs
Partially answering a question of Paul Seymour, we obtain a sufficient eigenvalue condition for the existence of k edge-disjoint spanning trees in a regular graph, when k ∈ {2, 3}. More precisely, we show that if the second largest eigenvalue of a d-regular graph G is less than d − 2k−1 d+1 , then G contains at least k edge-disjoint spanning trees, when k ∈ {2, 3}. We construct examples of grap...
متن کاملEdge Disjoint Spanning Trees ∗
Let Zm be the cyclic group of order m ≥ 3. A graph G is Zm-connected if G has an orientation D such that for any mapping b : V (G) 7→ Zm with ∑ v∈V (G) b(v) = 0, there exists a mapping f : E(G) 7→ Zm − {0} satisfying ∑ e∈E+ D (v) f(e) − ∑ e∈E− D (v) f(e) = b(v) in Zm for any v ∈ V (G); and a graph G is strongly Zm-connected if, for any mapping θ : V (G) → Zm with ∑ v∈V (G) θ(v) = |E(G)| in Zm, ...
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: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.11.039