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    • Film
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    A matroid extension result

    Oxley, James G.
    DataCite
    Disponible
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    Titre: A matroid extension result
    Auteur: Oxley, James G.
    Contributeur: Hennenfent, Guillaume
    Editeur: CIRM
    Date: 2018
    Sujet: 05b35 ; Combinatoires
    Description: Let $(A,B)$ be a $3$-separation in a matroid $M$. If $M$ is representable, then, in the underlying projective space, there is a line where the subspaces spanned by $A$ and $B$ meet, and $M$ can be extended by adding elements from this line. In general, Geelen, Gerards, and Whittle proved that $M$ can be extended by an independent set $\{p,q\}$ such that $\{p,q\}$ is in the closure of each of $A$ and $B$. In this extension, each of $p$ and $q$ is freely placed on the line $L$ spanned by $\{p,q\}$. This talk will discuss a result that gives necessary and sufficient conditions under which a fixed element can be placed on $L$....
    Identifiant: 10.24350/CIRM.V.19449503 (DOI)

    • Livre
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    Matroid theory

    Oxley, James G
    Oxford ; New York : Oxford University Press
    2011
    Recherche de la disponibilité
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    Titre: Matroid theory / James G. Oxley
    Auteur: Oxley, James G
    Edition: 2nd ed..
    Editeur: Oxford ; New York : Oxford University Press
    Date: 2011
    Collation: xiii, 684 p. : ill. ; 24 cm.
    Collection: Oxford graduate texts in mathematics ; 21
    Documents dans cette collection: Oxford graduate texts in mathematics
    Sujet LCSH: Matroids
    Note: Includes bibliographical references (p. [608]-638) and index.
    Classification: ams 05
    IMATH A-3
    Identifiant: 0198566948 (hbk.) (ISBN); 0199603391 (pbk.) (ISBN); 9780198566946 (hbk.) (ISBN); 9780199603398 (pbk.) (ISBN)
    No RERO: R006011687
    Permalien:
    http://data.rero.ch/01-R006011687/html?view=FR_V1

    • Article
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    Threshold distribution functions for some random representable matroids

    Oxley, James G
    Mathematical Proceedings of the Cambridge Philosophical Society, 1984, Vol.95(2), pp.335-347 [Revue évaluée par les pairs]
    Cambridge University Press
    Disponible
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    Titre: Threshold distribution functions for some random representable matroids
    Auteur: Oxley, James G
    Echelle: 1984
    Sujet: Sciences (General) ; Physics ; Mathematics;
    Description: A random submatroid ω r of the projective geometry PG ( r − 1, q ) is obtained from PG ( r − 1, q ) by deleting elements so that each element has, independently of all other elements, probability 1 − p of being deleted and probability p of being retained. The properties of such random structures were studied in [5] and [6]. In the first of these papers, p was kept fixed, while in the second, motivated by Erdös and Rényi's work ([3), [4]) on random graphs, p was taken to be a function of r . A recent paper of Bollobás[2] strengthens and extends a number of the results of Erdös and Rényi. In this paper we prove matroid analogues of several of Bollobàs's results thereby extending some of the results of [6].
    Précédemment: 198403
    Fait partie de: Mathematical Proceedings of the Cambridge Philosophical Society, 1984, Vol.95(2), pp.335-347
    Classement: 198403
    Identifiant: 0305-0041 (ISSN); 1469-8064 (E-ISSN); 10.1017/S0305004100061612 (DOI)

    • Article
    Sélectionner

    On a matroid generalization of graph connectivity

    Oxley, James G
    Mathematical Proceedings of the Cambridge Philosophical Society, 1981, Vol.90(2), pp.207-214 [Revue évaluée par les pairs]
    Cambridge University Press
    Disponible
    Plus…
    Titre: On a matroid generalization of graph connectivity
    Auteur: Oxley, James G
    Echelle: 1981
    Sujet: Sciences (General) ; Physics ; Mathematics;
    Description: This paper relates the concept of n -connection for graphs to Tutte's theory of n -connection for matroids (12). In particular, we show how Tutte's definition may be modified to give a matroid concept directly generalizing the graph-theoretic notion of n -connection.
    Précédemment: 198109
    Fait partie de: Mathematical Proceedings of the Cambridge Philosophical Society, 1981, Vol.90(2), pp.207-214
    Classement: 198109
    Identifiant: 0305-0041 (ISSN); 1469-8064 (E-ISSN); 10.1017/S0305004100058667 (DOI)

    • Plusieurs versions

    Ternary paving matroids

    Oxley, James G
    Discrete Mathematics, 1991, Vol.91(1), pp.77-86 [Revue évaluée par les pairs]
    ScienceDirect Journals (Elsevier)
    • Plusieurs versions

    On Minors Avoiding Elements in Matroids

    Oxley, James G
    European Journal of Combinatorics, November 1991, Vol.12(6), pp.531-539 [Revue évaluée par les pairs]
    ScienceDirect Journals (Elsevier)
    • Plusieurs versions

    A characterization of a class of non-binary matroids

    Oxley, James G
    Journal of Combinatorial Theory, Series B, 1990, Vol.49(2), pp.181-189 [Revue évaluée par les pairs]
    ScienceDirect Journals (Elsevier)
    • Plusieurs versions

    On an excluded-minor class of matroids

    Oxley, James G
    Discrete Mathematics, 1990, Vol.82(1), pp.35-52 [Revue évaluée par les pairs]
    ScienceDirect Journals (Elsevier)
    • Plusieurs versions

    A note on Negami's polynomial invariants for graphs

    Oxley, James G
    Discrete Mathematics, 1989, Vol.76(3), pp.279-281 [Revue évaluée par les pairs]
    ScienceDirect Journals (Elsevier)
    • Plusieurs versions

    On the matroids representable over GF(4)

    Oxley, James G
    Journal of Combinatorial Theory, Series B, 1986, Vol.41(2), pp.250-252 [Revue évaluée par les pairs]
    ScienceDirect Journals (Elsevier)