Landau's inequalities for tournament scores and a short proof of a theorem on transitive sub-tournaments

By Richard A. Brualdi, Jian Shen. 2001

85 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/94d3bbc80affb933c55d2ad78610190678b4f5a6

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Citations in the corpus

Hyperbolic and Parabolic Unimodular Random Maps (2016, background): “it (v) = M(v) = 2ˇ (v): SeeFigure 4for examples. This combinatorial denition of curvature is well-known and (in the deterministic setting) has been extensively studied in the literature, see e.g. [26, 3, 45] and references therein. We dene the average curvature of a unimodular random rooted map (M;ˆ”
There exist graphs with super-exponential Ramsey multiplicity constant (2008, background): “Consequently, a scaled Gromov hyperbolic graph would consist, locally around a vertex va, of m-gons glued along common edges incident upon va. As such, this local structure allows for a connection with a local graph curvature concept [7, 9 , 23], a concept heavily dependent on the number of edges o”
Bakry–Émery curvature and diameter bounds on graphs (2016, background): “However, for many discrete curvature notions there is already a BonnetMyers-type result established (for sectional curvature on planar graphs, see [6, 10, 14, 22], and for Ollivier-Ricci-curvature, see [20], and for Forman’s discrete Ricci curvature, see [8]).”
An asymptotic version of a conjecture by Enomoto and Ota (2010, background): “Brualdi and Shen [8] gave a simple proof of Theorem 1.”
Mass transportation and rough curvature bounds for discrete spaces (2009, background): “There are various notions of combinatorial curvature for graphs in the literature, see for instance [3,5,6].”
Volume growth, spectrum and stochastic completeness of infinite graphs (2011, background): “Several other notions of curvature have been introduced for planar graphs [4, 5, 31], cell complexes [21], and general metric measure spaces [8, 43, 45, 49, 50].”
Cheeger inequalities for unbounded graph Laplacians (2012, background): “While, for regular planar tessellations, isoperimetric constants can be computed explicitly [26, 28]; for arbitrary planar tessellations there are estimates in terms of curvature [27, 35, 40, 47].”