Results 61 to 70 of about 759 (82)
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Supereulerian regular matroids without small cocircuits
Journal of Graph Theory, 2022AbstractA cycle of a matroid is a disjoint union of circuits. A matroid is supereulerian if it contains a spanning cycle. To answer an open problem of Bauer in 1985, Catlin proved in [J. Graph Theory 12 (1988) 29–44] that for sufficiently large , every 2‐edge‐connected simple graph with and minimum degree is supereulerian. In [Eur. J. Combinatorics,
Huo, Bofeng +5 more
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Separating cocircuits in binary matroids
Linear Algebra and Its Applications, 1982 AbstractA cocircuit of a matroid is separating if deleting it leaves a separable matroid. We give an effecient algorithm which finds a separating cocircuit or a Fano minor in a binary matroid, thus proving constructively a theorem of Tutte. Using this algorithm and a new recursive characterization of bond matroids, we give a new method for testing ...
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Circuit and cocircuit partitions of binary matroids [PDF]
Czechoslovak Mathematical Journal, 2006 We give an example of a class of binary matroids with a cocircuit partition and we give some characteristics of a set of cocircuits of such binary matroids which forms a partition of the ground set.
Eunice G Mphako-Banda
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On cocircuit covers of bicircular matroids
Discrete Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
McNulty, Jennifer, Neudauer, Nancy Ann
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Some Small Circuit-Cocircuit Ramsey Numbers for Matroids
Combinatorics, Probability and Computing, 1995Ramsey numbers for matroids, which mimic properties of Ramsey numbers for graphs, have been denned as follows. Let k and l be positive integers. Then n(k, l) is the least positive integer n such that every connected matroid with n elements contains either a circuit with at least k elements or a cocircuit with at least l elements.
Hurst, Fair Barbour, Reid, Talmage James
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Matroids with many small circuits and cocircuits
Advances in Applied Mathematics, 2019Abstract Tutte proved that a non-empty 3-connected matroid with every element in a 3-element circuit and a 3-element cocircuit is either a whirl or the cycle matroid of a wheel. This result led to the Splitter Theorem. More recently, Miller proved that a matroid of sufficient size with every pair of elements in a 4-element circuit and a 4-element ...
Charles Semple
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On the Cocircuit Graph of an Oriented Matroid [PDF]
Discrete and Computational Geometry, 2000 The authors consider the cocircuit graph \(G_{\mathcal M}\) of an oriented matroid \(\mathcal M\), the 1-skeleton of the cell complex \(\mathcal W\) formed by the span of the cocircuits of \(\mathcal M\). In general, \(\mathcal W\) is not determined by \(G_{\mathcal M}\). The main result of the paper is the proof that if the vertex set (resp. edge set)
Cordovil, R. +2 more
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On the Circuit-cocircuit Intersection Conjecture
Graphs and Combinatorics, 2006Oxley has conjectured that for k≥4, if a matroid M has a k-element set that is the intersection of a circuit and a cocircuit, then M has a (k−2)-element set that is the intersection of a circuit and a cocircuit. In this paper we prove a stronger version of this conjecture for regular matroids.
S. R. Kingan, Manoel Lemos
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Partitioning Matroids with Only Small Cocircuits
Combinatorics, Probability and Computing, 2002We show that, for every positive integer c*, there is an integer n such that, if M is a matroid whose largest cocircuit has size c*, then E(M) can be partitioned into two sets E1 and E2 such that every connected component of each of M[mid ]E1 and M[mid ]E2 has at most n elements.
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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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