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Boundeddegree graphs have arbitrarily large queuenumber
, 2008
"... It is proved that there exist graphs of bounded degree with arbitrarily large queuenumber. In particular, for all ∆ ≥ 3 and for all sufficiently large n, there is a simple ∆regular nvertex graph with queuenumber at least c √ ∆n 1/2−1/∆ for some absolute constant c. ..."
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Cited by 2 (1 self)
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It is proved that there exist graphs of bounded degree with arbitrarily large queuenumber. In particular, for all ∆ ≥ 3 and for all sufficiently large n, there is a simple ∆regular nvertex graph with queuenumber at least c √ ∆n 1/2−1/∆ for some absolute constant c.
Spanning Star Trees In Regular Graphs
"... For a subset W of vertices of an undirected graph G, let S(W ) be the subgraph consisting of W , all edges incident to at least one vertex in W , and all vertices adjacent to at least one vertex in W . If S(W ) is a tree containing all the vertices of G, then we call it a spanning star tree of G. I ..."
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Cited by 1 (1 self)
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. In this case W forms a weakly connected but strongly acyclic dominating set for G. We prove that for every r # 3, there exist rregular nvertex graphs that have spanning star trees, and there exist rregular nvertex graphs that do not have spanning star trees, for all n su#ciently large (in terms of r
Enumerating all Hamilton Cycles and Bounding the Number of Hamilton Cycles in 3Regular Graphs
, 2011
"... We describe an algorithm which enumerates all Hamilton cycles of a given 3regular nvertex graph in time O(1.276 n), improving on Eppstein’s previous bound. The resulting new upper bound of O(1.276 n) for the maximum number of Hamilton cycles in 3regular nvertex graphs gets close to the best know ..."
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Cited by 1 (0 self)
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We describe an algorithm which enumerates all Hamilton cycles of a given 3regular nvertex graph in time O(1.276 n), improving on Eppstein’s previous bound. The resulting new upper bound of O(1.276 n) for the maximum number of Hamilton cycles in 3regular nvertex graphs gets close to the best
GRAPHS CONTAINING EVERY 2FACTOR
"... Abstract. For a graph G, let σ2(G) = min{d(u) + d(v) : uv / ∈ E(G)}. We prove that every nvertex graph G with σ2(G) ≥ 4n/3−1 contains each 2regular nvertex graph. This extends a theorem due to Aigner and Brandt and to Alon and Fisher. 1. ..."
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Abstract. For a graph G, let σ2(G) = min{d(u) + d(v) : uv / ∈ E(G)}. We prove that every nvertex graph G with σ2(G) ≥ 4n/3−1 contains each 2regular nvertex graph. This extends a theorem due to Aigner and Brandt and to Alon and Fisher. 1.
A Note on Random Minimum Length Spanning Trees
 JOURNAL OF COMBINATORICS
, 2000
"... Consider a connected rregular nvertex graph G with random independent edge lengths, each uniformly distributed on [0, 1]. Let rest(G) be the expected length of a minimum spanning tree. We show in this paper that if G is sufficiently highly edge connected then the expected length of a minimum sp ..."
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Cited by 10 (4 self)
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Consider a connected rregular nvertex graph G with random independent edge lengths, each uniformly distributed on [0, 1]. Let rest(G) be the expected length of a minimum spanning tree. We show in this paper that if G is sufficiently highly edge connected then the expected length of a minimum
Random minimum length spanning trees in regular graphs
"... Consider a connected rregular nvertex graph G with random independent edge lengths, each uniformly distributed on (0;1). Let mst(G) be the expected length of a minimum spanning tree. We show that mst(G) can be estimated quite accurately under two distinct circumstances. Firstly, if r is large and ..."
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Cited by 21 (9 self)
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Consider a connected rregular nvertex graph G with random independent edge lengths, each uniformly distributed on (0;1). Let mst(G) be the expected length of a minimum spanning tree. We show that mst(G) can be estimated quite accurately under two distinct circumstances. Firstly, if r is large
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Critical random graphs: diameter and mixing time
"... Abstract. Let C1 denote the largest connected component of the critical ErdősRényi random graph G(n, 1). We show that, typically, the diameter of C1 is of n order n 1/3 and the mixing time of the lazy simple random walk on C1 is of order n. The latter answers a question of Benjamini, Kozma and Worm ..."
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Cited by 20 (7 self)
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and Wormald [5]. These results extend to clusters of size n 2/3 of pbond percolation on any dregular nvertex graph where such clusters exist, provided that p(d − 1) ≤ 1 + O(n −1/3). 1.
A note on random minimum length spanning trees. The Electronic
 Journal of Combinatorics
, 2000
"... Consider a connected rregular nvertex graph G with random independent edge lengths, each uniformly distributed on [0,1]. Let mst(G) be the expected length of a minimum spanning tree. We show in this paper that if G is sufficiently highly edge connected then the expected length of a minimum spannin ..."
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Consider a connected rregular nvertex graph G with random independent edge lengths, each uniformly distributed on [0,1]. Let mst(G) be the expected length of a minimum spanning tree. We show in this paper that if G is sufficiently highly edge connected then the expected length of a minimum
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Results 1  10
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