Many large eigenvalues in sparse graphs
نویسندگان
چکیده
منابع مشابه
Graphs with many valencies and few eigenvalues
Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct connected graphs with four and five distinct eigenvalues and arbitrarily many distinct valencies. The graphs with four distinct eigenvalues come from regular two-graphs. As a side result, we characterize the disconne...
متن کاملSparse random graphs: Eigenvalues and eigenvectors
In this paper we prove the semi-circular law for the eigenvalues of regular random graph Gn,d in the case d→∞, complementing a previous result of McKay for fixed d. We also obtain a upper bound on the infinity norm of eigenvectors of Erdős-Rényi random graph G(n, p), answering a question raised by Dekel-Lee-Linial.
متن کاملBraess's Paradox in Large Sparse Graphs
Braess’s paradox, in its original context, is the counter-intuitive observation that, without lessening demand, closing roads can improve traffic flow. With the explosion of distributed (selfish) routing situations understanding this paradox has become an important concern in a broad range of network design situations. However, the previous theoretical work on Braess’s paradox has focused on “d...
متن کاملLarge Cliques in Sparse Random Intersection Graphs
Given positive integers n and m, and a probability measure P on {0, 1, . . . ,m}, the random intersection graph G(n,m,P ) on vertex set V = {1, 2, . . . , n} and with attribute set W = {w1, w2, . . . , wm} is defined as follows. Let S1, S2, . . . , Sn be independent random subsets of W such that for any v ∈ V and any S ⊆ W we have P(Sv = S) = P (|S|)/ ( m |S| ) . The edge set of G(n,m,P ) consi...
متن کاملLarge induced forests in sparse graphs
For a graph G, let a(G) denote the maximum size of a subset of vertices that induces a forest. Suppose that G is connected with n vertices, e edges, and maximum degree ∆. Our results include: (a) if ∆ ≤ 3, and G 6= K4, then a(G) ≥ n−e/4−1/4 and this is sharp for all permissible e ≡ 3 (mod 4), (b) if ∆ ≥ 3, then a(G) ≥ α(G) + (n − α(G))/(∆ − 1)2. Several problems remain open.
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: European Journal of Combinatorics
سال: 2013
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2013.03.004