Results 31 to 40 of about 155 (58)
Circuits and structure in matroids and graphs [PDF]
, 2006 This dissertation consists of several results on matroid and graph structure and is organized into three main parts. The main goal of the first part, Chapters 1-3, is to produce a unique decomposition of 3-connected matroids into more highly connected ...
Beavers, Brian Daniel
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Unavoidable Minors of Large 4-Connected Bicircular Matroids [PDF]
, 2015 It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids.
Chun, Deborah +3 more
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Infinite graphic matroids Part I [PDF]
, 2013 An infinite matroid is graphic if all of its finite minors are graphic and the intersection of any circuit with any cocircuit is finite. We show that a matroid is graphic if and only if it can be represented by a graph-like topological space: that is, a ...
Bowler, Nathan +2 more
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Non-Separating Cocircuits and Graphicness in Matroids
, 2012 Let $M$ be a 3-connected binary matroid and let $Y(M)$ be the set of elements of $M$ avoiding at least $r(M)+1$ non-separating cocircuits of $M$. Lemos proved that $M$ is non-graphic if and only if $Y(M)\neq\emp$. We generalize this result when by establishing that $Y(M)$ is very large when $M$ is non-graphic and $M$ has no $M\s(K_{3,3}"')$-minor if $M$
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Capturing elements in matroid minors [PDF]
, 2011 In this dissertation, we begin with an introduction to a matroid as the natural generalization of independence arising in three different fields of mathematics. In the first chapter, we develop graph theory and matroid theory terminology necessary to the
Chun, Deborah
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Matroid and Tutte-connectivity in infinite graphs [PDF]
, 2012 We relate matroid connectivity to Tutte-connectivity in an infinite graph. Moreover, we show that the two cycle matroids, the finite-cycle matroid and the cycle matroid, in which also infinite cycles are taken into account, have the same connectivity ...
Bruhn, Henning
core
Detachable Pairs in 3-Connected Matroids
, 2015 The classical tool at the matroid theorist’s disposal when dealing with the common problem of wanting to remove a single element from a 3-connected matroid without losing 3-connectivity is Tutte’s Wheels-and-Whirls Theorem.
Williams, Alan
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Non-Separating Cocircuits Avoiding Some Elements
Annals of Combinatorics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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NON-SEPARATING CIRCUITS AND COCIRCUITS IN MATROIDS
2007Bráulio Maia Junior +2 more
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