Direct methods for sparse matrices
Direct methods for sparse matrices
On the second eigenvalue of random regular graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
Random trees and random graphs
proceedings of the eighth international conference on Random structures and algorithms
A New Implementation of Sparse Gaussian Elimination
ACM Transactions on Mathematical Software (TOMS)
On Vertex Ranking for Permutations and Other Graphs
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
On the order of countable graphs
European Journal of Combinatorics
Tree-depth, subgraph coloring and homomorphism bounds
European Journal of Combinatorics
On the threshold of having a linear treewidth in random graphs
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Forbidden graphs for tree-depth
European Journal of Combinatorics
Journal of Graph Theory
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Tree-depth is a parameter introduced under several names as a measure of sparsity of a graph. We compute asymptotic values of the tree-depth of a random graph on n vertices where each edge appears independently with probability p. For dense graphs, np-+~, the tree-depth of a random graph G is aastd(G)=n-O(n/p). Random graphs with p=c/n, have aaslinear tree-depth when c1, the tree-depth is @Q(logn) when c=1 and @Q(loglogn) for c1 is derived from the computation of tree-width and provides a more direct proof of a conjecture by Gao on the linearity of tree-width recently proved by Lee, Lee and Oum (2012) [15]. We also show that, for c=1, every width parameter is aasconstant, and that random regular graphs have linear tree-depth.