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Arrangements Of Minors In The Positive Grassmannian And a Triangulation of The Hypersimplex [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities and inequalities between the minors in the positive Grassmannian.
Miriam Farber, Yelena Mandelshtam
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The sandpile group of a thick cycle graph
Electronic Journal of Graph Theory and Applications, 2022 The majority of graphs whose sandpile groups are known are either regular or simple. We give an explicit formula for a family of non-regular multi-graphs called thick cycles. A thick cycle graph is a cycle where multi-edges are permitted.
Diane Christine Alar +4 more
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Internally 4-Connected Graphs With No {Cube, V8}-Minor
Discussiones Mathematicae Graph Theory, 2021 A simple graph is a minor of another if the first is obtained from the second by deleting vertices, deleting edges, contracting edges, and deleting loops and parallel edges that are created when we contract edges.
Lewchalermvongs Chanun +1 more
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Implications of network topology on stability. [PDF]
PLoS ONE, 2015 In analogy to chemical reaction networks, I demonstrate the utility of expressing the governing equations of an arbitrary dynamical system (interaction network) as sums of real functions (generalized reactions) multiplied by real scalars (generalized ...
Ali Kinkhabwala
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Structure of Projective Planar Subgraphs of the Graph Obstructions for Fixed Surface
Кібернетика та комп'ютерні технології, 2022 Consider the problem of studying the metric properties of a subgraph G \ v, where v is an arbitrary vertex of obstruction graphs G of a nonorientable genus, which will determine the sets of points of attachment of one subgraph to another and allow ...
Volodymyr Petrenjuk +2 more
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Two lower bounds for $p$-centered colorings [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Given a graph $G$ and an integer $p$, a coloring $f : V(G) \to \mathbb{N}$ is \emph{$p$-centered} if for every connected subgraph $H$ of $G$, either $f$ uses more than $p$ colors on $H$ or there is a color that appears exactly once in $H$. The notion of $
Loïc Dubois +4 more
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Shift operators from the simplex representation in momentum-space CFT
Journal of High Energy Physics, 2023 We derive parametric integral representations for the general n-point function of scalar operators in momentum-space conformal field theory. Recently, this was shown to be expressible as a generalised Feynman integral with the topology of an (n − 1 ...
Francesca Caloro, Paul McFadden
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Consensus analysis of the weighted corona networks
Frontiers in Physics, 2022 The consensus of complex networks has attracted the attention of many scholars. The graph operation is a common method to construct complex networks, which is helpful in studying the consensus of complex networks. Based on the corona networks G1◦G2, this
Weiwei Du +3 more
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Capturing Polynomial Time using Modular Decomposition [PDF]
Logical Methods in Computer Science, 2019 The question of whether there is a logic that captures polynomial time is one of the main open problems in descriptive complexity theory and database theory.
Berit Grußien
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Asymptotic properties of some minor-closed classes of graphs (conference version) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Let $\mathcal{A}$ be a minor-closed class of labelled graphs, and let $G_n$ be a random graph sampled uniformly from the set of n-vertex graphs of $\mathcal{A}$. When $n$ is large, what is the probability that $G_n$ is connected? How many components does
Mireille Bousquet-Mélou, Kerstin Weller
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