Results 111 to 120 of about 4,343 (225)
Tutte's first colour-cycle conjecture
, 1975 Includes bibliographical references.This thesis presents a proof of Conjecture I (see Section 35) of W. T. Tutte's paper "A contribution to the theory of chromatic polynomials''.
Kilpatrick, Peter Allan
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Journal of Combinatorial Theory, Series B, 1978 AbstractIn this paper, the basic properties of oriented matroids are examined. A topological representation theorem for oriented matroids is proven, utilizing the notion of an “arrangement of pseudo-hemispheres”. The duality theorem of linear programming is extended to oriented matroids.
Jon Folkman, Jim Lawrence
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Fork-decompositions of matroids [PDF]
, 2004 For the abstract of this paper, please see the PDF ...
Whittle, G +11 more
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Partial Matroid Representations
, 1984 A central theorem of matroid 3-connectivity is established that has a number of new and old connectivity results as corollaries.
Truemper, Klaus
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Enumerating matroid extensions [PDF]
, 2023 This thesis investigates the problem of enumerating the extensions of certain matroids. A matroid M is an extension of a matroid N if M delete e is equal to N for some element e of M. Similarly, a matroid M is a coextension of a matroid N if M contract e
Redlin Hume, Shayla
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Aspects of Matroid Connectivity [PDF]
, 2014 Connectivity is a fundamental tool for matroid theorists, which has become increasingly important in the eventual solution of many problems in matroid theory. Loosely speaking, connectivity can be used to help describe a matroid's structure.
Brettell, Nicholas John
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Valuations for Matroid Polytope Subdivisions
, 2010 We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.
Federico Ardila +2 more
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Discrete Mathematics, 1995 This communication is an announcement of results for \(h\)-vectors of matroids which settle a conjecture of Stanley.
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Discrete Mathematics, 1981 AbstractWe show, by means of counterexamples, that products with rank rk(M)rk(N) of a matroid M by a matroid N do not exist in general, and that there is no free-est product of M by N. We prove that a canonical product of M by N (having rank rk(M)+rk(N)−1) is a free-est product in a certain (weaker) sense.
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Matroid Optimization and Algorithms
, 1990 This paper reviews matroid optimization and algorithms including applications of matroid intersection; submodular functions and polymatroids; submodular flows and other general models; matroid connectivity algorithms; recognition of representability; and
Cunningham, William H., Bixby, Robert E.
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