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Publikováno v:
Journal of Combinatorial Theory, Series B. 152:80-120
Generalizing a graph-theoretical result of Maffray to binary matroids, Oxley and Wetzler proved that a connected simple binary matroid M has no odd circuits other than triangles if and only if M is affine, M is isomorphic to M ( K 4 ) or F 7 , or M i
Autor:
Pirouz Naiyer
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 35, Iss 1, Pp 95-104 (2015)
In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.
Externí odkaz:
https://doaj.org/article/f2fb162e1323419d9a7d4df55e70f6b7
Autor:
Rigoberto Flórez
We study a generalization of the concept of harmonic conjugation from projective geometry and full algebraic matroids to a larger class of matroids called \emph{harmonic matroids}. We use harmonic conjugation to construct a projective plane of prime
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d8e76d736521f009a616a80552ff08e
http://arxiv.org/abs/2202.09416
http://arxiv.org/abs/2202.09416
Publikováno v:
SIAM Journal on Discrete Mathematics. 34:1522-1537
A connected matroid $M$ is unbreakable if, for each of its flats $F$, the matroid $M/F$ is connected or, equivalently, if $M^*$ has no two skew circuits. Pfeil showed that a simple graphic matroid ...
Autor:
Dennis Hall
Publikováno v:
Journal of Combinatorial Theory, Series B. 139:296-315
It is well known that, for any integer n greater than one, there is a number r such that every 2-connected simple graph with at least r edges has a minor isomorphic to an n-edge cycle or K 2 , n . This result was extended to matroids by Lovasz, Schri
Publikováno v:
Advances in Combinatorics.
DeVos, Kwon, and Oum introduced the concept of branch-depth of matroids as a natural analogue of tree-depth of graphs. They conjectured that a matroid of sufficiently large branch-depth contains the uniform matroid $U_{n,2n}$ or the cycle matroid of
Publikováno v:
Advances in Applied Mathematics. 105:1-24
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 matr
Autor:
Ben Smith, Iain Moffatt
Publikováno v:
Journal of Combinatorial Theory, Series B. 133:1-31
We introduce the notion of a delta-matroid perspective. A delta-matroid perspective consists of a triple ( M , D , N ) , where M and N are matroids and D is a delta-matroid such that there are strong maps from M to the upper matroid of D and from the
Autor:
Thomas Thierauf, Rohit Gurjar
Publikováno v:
STOC
Given two matroids on the same ground set, the matroid intersection problem asks to find a common independent set of maximum size. In case of linear matroids, the problem had a randomized parallel algorithm but no deterministic one. We give an almost