Modern Graph Theory

By L. Beineke, Robin J. Wilson. 2013

1,706 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

NLS ground states on graphs (2014, background): “We recall that a trail in a graph (see [7]) is a finite sequence of consecutive edges, in which no edge is repeated (note that a vertex, instead, may be repeated, if the trail contains cycles or self-loops).”
Fully Distributed State Estimation for Wide-Area Monitoring Systems (2012, background): “S. Kar is with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 USA (e-mail: soummyak@andrew.cmu.edu).”
The chromatic thresholds of graphs (2011, background): “Most is standard (see [6], for example); we shall repeat nonstandard definitions when they are first used.”
Distributed Parameter Estimation in Sensor Networks: Nonlinear Observation Models and Imperfect Communication (2008, background): “…this is achieved by intermittent dataexchanges among the sensors, whereby each sensor fuses its version of the estimate from time to time with thosef other sensors with which it can communicate (in this context, see [1], [2], [3], [4], for a treatment of general distributed stochastic algorithms.)”
Every finite group is the group of self-homotopy equivalences of an elliptic space (2011, background): “For the basic facts about graphs, we refer to [9].”
A Survey on Quantum Channel Capacities (2018, background): “e) The Zero-Error Classical Capacity: The properties of zero-error communication systems are discussed in Shannon’s famous paper on the zero-error capacity of a noisy channel [478], in the work of Körner and Orlitsky on zero-error information theory [283], and in the work of Bollobás on modern graph”
Some new results in extremal graph theory (2011, background): “For background on this lemma we refer the reader to [7], Section IV.”
ALGEBRAIC CONNECTIVITY OF ERDÖS-RÉNYI GRAPHS NEAR THE CONNECTIVITY THRESHOLD (2014, background): “There is a large literature on Erdös-Rényi graphs [18, 6, 23, 1] and, in particular, their spectral properties [19, 28, 29].”
Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs (2010, background): “For an in-depth treatment of the background material, we suggest [6].”
Spectral radius and Hamiltonicity of graphs with large minimum degree (2016, background): “For graph notation and terminology undefined here we refer the reader to [2].”
Recommender Systems (2012, background): “Mathematically speaking, a network G is an ordered pair of disjoint sets (V,E) where V is the set of nodes and the set of edges, E, is a subset of V × V [56].”