Studies in foundations and combinatorics
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The structural and algorithmic study of stability in nonexpansive networks is based on a representation of the possible assignments of Boolean values for a network as vertices in a Boolean hypercube under the associated Hamming metric. This global view takes advantage of the med…
The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their end. The 1-ended graphs in this class were id…
Any finite abstract group can be realized as the automorphism group of a graph. The purpose of this memoir is to find the realization, for each finite abelian group, with the least number of vertices possible. The results are extended to all finite abelian groups. Thus a complet…
Given a partial symmetric matrix, the positive definite completion problem asks if the unspecified entries in the matrix can be chosen so as to make the resulting matrix positive definite. The positive definite completion problem can also be viewed as a mechanism for addressing …
A theory of counting nonintersecting lattice paths by the major index and its generalizations is developed. We obtain determinantal expressions for the corresponding generating functions for families of nonintersecting lattice paths with given starting points and given final poi…
Many sequences of combinatorial interest are known to be unimodal or log-concave and there has been a considerable amount of interest devoted to this topic. The main object of this work is to point out another branch of mathematics that can be successfully used to attack these k…
For each infinite cardinal [lowercase Greek]Kappa, we give a structural characterization of the graphs with no [italic capital]K[subscript lowercase Greek]Kappa minor. We also give such a characterization of the graphs with no "half-grid" minor.
We define an orthogonal basis in the space of real-valued functions of a random graph, and prove a functional limit theorem for this basis. Limit theorems for other functions then follow by decomposition. The results include limit theorems for the two random graph models [italic…
This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields. Major concepts are illustrated with runnin…
Edge-colourings of graphs
by Wilson, Robin J., Fiorini, Stanley
fromResearch Notes in Mathematics
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Type: Book
Graph theory is a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or any graph representing relations in massive data sets. This book explains the universal and ubiquitous coh…
