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The rigidity of infinite graphs [PDF]
Discrete & Computational Geometry, 2013 A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite simple graphs in R^d with respect to the classical l^p norms, for d>1 and ...
Kitson, D., Power, S. C.
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Spectral partitions on infinite graphs [PDF]
Journal of Physics A: Mathematical and General, 2000 Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well defined ...
Alexander S +8 more
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Helmholtz operators on infinite graphs [PDF]
HeliyonThe Helmholtz equation in its simplest form is Δu(a)=−k2u(a). In this note, we study a generalized discrete version of this equation on an infinite graph, by using potential-theoretic methods.
Varadha Raj Manivannan +1 more
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Characterizing Omega-Regularity through Finite-Memory Determinacy of Games on Infinite Graphs [PDF]
TheoretiCS, 2023 We consider zero-sum games on infinite graphs, with objectives specified as sets of infinite words over some alphabet of colors. A well-studied class of objectives is the one of $\omega$-regular objectives, due to its relation to many natural problems in
Patricia Bouyer +2 more
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Matchings on infinite graphs [PDF]
Probability Theory and Related Fields, 2011 Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching.
C Bordenave +14 more
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Infinite matroids in graphs [PDF]
Discrete Mathematics, 2011 It has recently been shown that infinite matroids can be axiomatized in a way that is very similar to finite matroids and permits duality. This was previously thought impossible, since finitary infinite matroids must have non-finitary duals.
Bruhn, Henning, Diestel, Reinhard
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Journal of Combinatorial Theory, 1967 AbstractThis expository article describes work which has been done on various problems involving infinite graphs, mentioning also a few unsolved problems or suggestions for future investigation.
C. St. J. A. Nash‐Williams
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Distinguishing homomorphisms of infinite graphs [PDF]
Contributions to Discrete Mathematics, 2012 We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph $
Bonato, Anthony, Delic, Dejan
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On external presentations of infinite graphs [PDF]
Electronic Proceedings in Theoretical Computer Science, 2009 The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices.
Christophe Morvan
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On arithmetic infinite graphs [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2000 We compute explicitly the Selberg trace formula for principal congruence subgroups $\Gamma$ of $PGL(2, \mathbf{F}_q[t])$, which is the modular group in positive characteristic cases. It is known that $\Gamma \backslash X$ is an infinite Ramanujan diagram, where $X$ is the $q + 1$-regular tres.
Hirofumi Nagoshi
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