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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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The Minor Crossing Number of Graphs with an Excluded Minor [PDF]
The Electronic Journal of Combinatorics, 2008 The minor crossing number of a graph $G$ is the minimum crossing number of a graph that contains $G$ as a minor. It is proved that for every graph $H$ there is a constant $c$, such that every graph $G$ with no $H$-minor has minor crossing number at most $c|V(G)|$.
Bokal, Drago +2 more
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The probability of planarity of a random graph near the critical point [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Erdős and Rényi conjectured in 1960 that the limiting probability $p$ that a random graph with $n$ vertices and $M=n/2$ edges is planar exists. It has been shown that indeed p exists and is a constant strictly between 0 and 1.
Marc Noy +2 more
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Theoretical Computer Science, 2011 Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph act upon the dynamics of the classical Minority rule.
Rouquier, Jean-Baptiste +2 more
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Stem Cell Research & Therapy, 2021 Background We explored whether stem cell therapy was effective for animal models and patients with Crohn’s disease (CD). Methods We searched five online databases. The relative outcomes were analyzed with the aid of GetData Graph Digitizer 2.26 and Stata
Ruo Wang +7 more
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Ribbon Graph Minors and Low-Genus Partial Duals [PDF]
, 2015 We give an excluded minor characterisation of the class of ribbon graphs that admit partial duals of Euler genus at most one.
Iain Moffatt
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Inverse Eigenvalue Problems for Two Special Acyclic Matrices
Mathematics, 2016 In this paper, we study two inverse eigenvalue problems (IEPs) of constructing two special acyclic matrices. The first problem involves the reconstruction of matrices whose graph is a path, from given information on one eigenvector of the required matrix
Debashish Sharma, Mausumi Sen
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Discrete Applied Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Reinhard Diestel, Daniela Kühn
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Graph Minors and Minimum Degree [PDF]
The Electronic Journal of Combinatorics, 2010 Let $\mathcal{D}_k$ be the class of graphs for which every minor has minimum degree at most $k$. Then $\mathcal{D}_k$ is closed under taking minors. By the Robertson-Seymour graph minor theorem, $\mathcal{D}_k$ is characterised by a finite family of minor-minimal forbidden graphs, which we denote by $\widehat{\mathcal{D}}_k$.
Gasper Fijavz, David R. Wood
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The Scientific World Journal, 2014 An n×n matrix is called an N0-matrix if all its specified principal minors are nonpositive. In the context of partial matrices, a partial matrix is called a partial N0-matrix if all its specified principal minors are nonpositive.
Cristina Jordán, Juan R. Torregrosa
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