Digraphs - theory, algorithms and applications

By Jørgen Bang-Jensen, Gregory Z. Gutin. 2002

2,068 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7cb0827142e9b129ed231b3aee2a083f582be568

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Citations in the corpus

Necessary and sufficient graphical conditions for formation control of unicycles (2005, background): “i 9 j for all i 2 U and j 2 V U , then U is said to be closed. More information can be found in [ 23 ],”
Atomic Cross-Chain Swaps (2018, background): “The protocol is easily extended to a model where there may be more than one arc from one vertex to another, so-called directed multi-graphs [2], reflecting the situation where Alice wants to transfer assets on distinct blockchains to Bob.”
Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity (2020, background): “More elaborate descriptions can be found in (Graham, Knuth, Patashnik, and Liu, 1989; West et al., 2001; Bang-Jensen and Gutin, 2008):”
Surveys in Combinatorics 2009: Embedding large subgraphs into dense graphs (2009, background): “ to (n − 1)/2. We can then greedily remove Hamilton cycles as long as the degrees satisfy the condition in Theorem 18.) It is the best bound so far towards the following conjecture of Kelly (see e.g. [10]). Conjecture 21. (Kelly) Every regular tournament on n vertices can be partitioned into (n −1)/”
Graph-Based Network Analysis of Resting-State Functional MRI (2010, unknown): “The descriptions for other types of graphs can be found in previous literature (Boccaletti et al., 2006; Bang-Jensen and Gutin, 2008).”
Monotone drawings of planar graphs (2004, methodology): “We use the standard terminology and notation on digraphs as given in [ 2 ].”
Graph Theory (2018, methodology): “We search for augmenting paths by constructing an alternating tree of a matching S which is a subtree of G such that (1) a vertex r (the root of the tree) is unmatched, (2) every second edge on each path out from r is in S and the remaining edges are not in S, and (3) either there is an augmenting p”
Structured Connectivity in Cerebellar Inhibitory Networks (2014, background): “…has been reported in other complex networks (Holland and Leinhardt, 1970; Milo et al., 2004), we tested this hypothesis in the MLI network and therefore grouped the patterns according to their property of transitivity (Bang-Jensen and Gutin, 2008; Supplemental Experimental Procedures; Figure S5A).”
Meta-modeling game for deriving theoretical-consistent, micro-structural-based traction-separation laws via deep reinforcement learning (2018, background): “Recall that a digraph D = (V, E) is an ordered pair of non-empty finite sets which consists of a vertex set V and an edge set E [Bang-Jensen and Gutin, 2008].”
An exact minimum degree condition for Hamilton cycles in oriented graphs (2008, background): “It is the best bound so far towards the classical conjecture of Kelly (see, for example, [3]), which states that every regular tournament on n vertices can be partitioned into (n − 1)/2 edge-disjoint Hamilton cycles.”
Leader-following coordination of multi-agent systems with coupling time delays (2007, background): “ desired constant velocity. If each agent is regarded as a node, then their coupling topology is conveniently described by a simple graph (basic concepts and notations of graph theory can be found in [13, 17, 10]). Let G = (V,E,A) be a weighted digraph of order n with the set of nodes V = {1,2,...,n”
The traveling salesman problem and its variations (2007, methodology): “3 The operation is called path-contraction in [ 6 ], but since we do not consider any other type of contraction, we will use the shorter name.”
Multilayer networks (2013, background): “For example, edges often exhibit heterogeneous features: they can be directed [15, 245, 350], have different strengths (i.”
Identification of Peer Effects through Social Networks (2009, unknown): “, Bang-Jensen and Cutin (2000). Say that there is a path between i and j in the network if Gij > 0 or if there exist i1, .”
Discrete Signal Processing on Graphs (2012, background): “For example, directed (acyclic) graphs [11], [12] represent Bayesian networks where each random variable is independent of others given the variables deﬁned on its parent nodes.”