• Corpus ID: 239024638

The smallest class of binary matroids closed under direct sums and complements

@inproceedings{Oxley2021TheSC,
  title={The smallest class of binary matroids closed under direct sums and complements},
  author={James G. Oxley and Jagdeep Singh},
  year={2021}
}
  • J. Oxley, Jagdeep Singh
  • Published 18 October 2021
  • Mathematics
The class of cographs or complement-reducible graphs is the class of graphs that can be generated from K1 using the operations of disjoint union and complementation. By analogy, this paper introduces the class of binary comatroids as the class of matroids that can be generated from the empty matroid using the operations of direct sum and taking complements inside of binary projective space. We show that a proper flat of a binary comatroid is a binary comatroid. Our main result identifies those… 

References

SHOWING 1-10 OF 17 REFERENCES
Connected Hyperplanes in Binary Matroids
TLDR
It is proved that any simple and cosimple connected binary matroid has at least four connected hyperplanes and each element in such a matroid is contained in at least two connected hyperplane.
A Linear Recognition Algorithm for Cographs
TLDR
This paper presents a linear time algorithm for recognizing cographs and constructing their cotree representation, which is possible to design very fast polynomial time algorithms for problems which are intractable for graphs in general.
Complement reducible graphs
On a property of the class of n-colorable graphs
Abstract An obvious lower bound on the chromatic number of a graph is the largest possible number of points in a complete subgraph. A sufficient condition is presented for these numbers to be equal.
Flows and generalized coloring theorems in graphs
  • F. Jaeger
  • Mathematics, Computer Science
    J. Comb. Theory, Ser. B
  • 1979
On a class of posets and the corresponding comparability graphs
  • H. A. Jung
  • Computer Science, Mathematics
    J. Comb. Theory, Ser. B
  • 1978
TLDR
The comparability graphs of multitrees are characterized and studied with respect to minimal path coverings to generalized to the notion of a multitree.
On matroid connectivity
  • W. Cunningham
  • Computer Science, Mathematics
    J. Comb. Theory, Ser. B
  • 1981
TLDR
Three types of matroid connectivity, including Tutte's, are defined and shown to generalize corresponding notions of graph connectivity, which are generalized to matroids.
Matroid theory
TLDR
The current status has been given for all the unsolved problems or conjectures that appear in Chapter 14 and the corrected text is given with the inserted words underlined.
‘G’
  • P. Alam
  • Composites Engineering: An A–Z Guide
  • 2021
Uniquely representable combinatorial geometries
  • Teorie Combinatorie
  • 1973
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