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On a new graph invariant and a criterion for planarity.
Yves Colin de Verdière
- pp 137-147
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[9] R. Bacher and Y. deVerdì ere: Multiplicités des valeurs propres and transformationsétoile-triangle des graphes, Bull.Abstract:
[9] R. Bacher and Y. Colin deVerdì ere: Multiplicités des valeurs propres et transformationsétoile-triangle des graphes, Bull.read more
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Book
Mesh Parameterization Methods and Their Applications
TL;DR: A survey of recent methods for creating piecewise linear mappings between triangulations in 3D and simpler domains such as planar regions, simplicial complexes, and spheres is presented in this article.
Proceedings ArticleDOI
Mesh parameterization: theory and practice
TL;DR: This course outlines its mathematical foundations, describes recent methods for parameterizing meshes over various domains, discusses emerging tools like global parameterization and inter-surface mapping, and demonstrates a variety of parameterization applications.
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Fundamentals of spherical parameterization for 3D meshes
TL;DR: A generalization of the method of barycentric coordinates for planar parameterization which solves the spherical parameterization problem is described, its correctness is proved by establishing a connection to spectral graph theory and how to compute these parameterizations is shown.
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The minimum rank of symmetric matrices described by a graph: A survey☆
Shaun M. Fallat,Leslie Hogben +1 more
TL;DR: The current state of knowledge on the problem of determining the minimum rank of a graph and related issues is surveyed.
Proceedings ArticleDOI
Mesh parameterization: theory and practice Video files associated with this course are available from the citation page
TL;DR: This course outlines its mathematical foundations, describes recent methods for parameterizing meshes over various domains, discusses emerging tools like global parameterization and inter-surface mapping, and demonstrates a variety of parameterization applications.
References
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Journal ArticleDOI
The ellipsoid method and its consequences in combinatorial optimization
TL;DR: The method yields polynomial algorithms for vertex packing in perfect graphs, for the matching and matroid intersection problems, for optimum covering of directed cuts of a digraph, and for the minimum value of a submodular set function.
Book
Random walks and electric networks
Peter G. Doyle,J. Laurie Snell +1 more
TL;DR: The goal will be to interpret Polya’s beautiful theorem that a random walker on an infinite street network in d-dimensional space is bound to return to the starting point when d = 2, but has a positive probability of escaping to infinity without returning to the Starting Point when d ≥ 3, and to prove the theorem using techniques from classical electrical theory.
Journal ArticleDOI
Approximating the permanent
Mark Jerrum,Alistair Sinclair +1 more
TL;DR: A randomised approximation scheme for the permanent of a 0–1s presented, demonstrating that the matchings chain is rapidly mixing, apparently the first such result for a Markov chain with genuinely c...
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Graph minors. III. Planar tree-width
Neil Robertson,Paul Seymour +1 more
TL;DR: It is proved that for any fixed planar graph H, every planar graphs with sufficiently large tree-width has a minor isomorphic to H.