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Chip-Firing and Rotor-Routing on Directed Graphs
Chip-Firing Rotor-Routing Directed Graphs
2015/8/14
We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguing op...
Continuous-time distributed convex optimization on directed graphs
Continuous-time convex optimization directed graphs Optimization and Control
2012/4/17
This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works ...
Normalized graph Laplacians for directed graphs
Normalized graph Laplacians directed graphs Combinatorics
2011/9/20
Abstract: We consider the normalized Laplacian for directed graphs with positive and negative edge weights. We derive basic spectral properties of the normalized Laplacian and identify extremal eigenv...
Chip-Firing and Riemann-Roch Theory for Directed Graphs
Chip-Firing Riemann-Roch Theory Directed Graphs
2011/1/17
We investigate Riemann-Roch theory for directed graphs. The Riemann-Roch criteria of Amini and
Manjunath is generalized to all integer lattices orthogonal to some positive vector. Using a generalized...
A directed graph is set-homogeneous if, whenever U and V are isomorphic finite subdigraphs, there is an automorphism g of the digraph with U^g=V. Here, extending work of Lachlan on finite homogeneous...
Long cycles in subgraphs of (pseudo)random directed graphs
Long cycles subgraphs of (pseudo)random directed graphs
2010/12/8
We study the resilience of random and pseudorandom directed graphs with respect to the property of having long directed cycles. For every 0 < < 1/2 we find a constant c = c(
) such that the followin...