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Classes of Matroids

Al- Hawary, Talal A., (2004) Classes of Matroids. Matematika, 20 (2). pp. 87-92. ISSN 01278274

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Official URL: http://www.fs.utm.my/matematika/images/stories/matematika/200420201.pdf

Affiliations

Mu’tah University, Jordan, Dept. of Mathematics and Statistics

Abstract

This paper explores which classes of graphs and matroids are k-balanced. A connection between k-balanced graphs and k-balanced matroids was also obtained. In this paper, we continue our study of the class of k-balanced matroids in order to see what matroid operations preserve k-balance. Since strong maps of matroids are defined as analogues of continuous maps of topological spaces, it is natural to ask what other topological notions carry over to matroids. In characterizing strong maps from 2000 to 2003, Al-Hawary defined a closure matroid to be a matroid in which A [ B = A[B for all subsets A and B of its ground set. We obtain a new classification of closure matroids. Moreover, necessary and sufficient conditions for the direct sum, parallel extension connection and series extension connection to preserve k-balance property are given. This paper explores which classes of graphs and matroids are k balanced. A connection between k-balanced graphs and k-balanced matroids was also obtained. In this paper, we continue our study of the class of k-balanced matroids in order to see what matroid operations preserve k-balance. Since strong maps of matroids are defined as analogues of continuous maps of topological spaces, it is natural to ask what other topological notions carry over to matroids. In characterizing strong maps from 2000 to 2003, Al-Hawary defined a closure matroid to be a matroid in which A [ B = A[B for all subsets A and B of its ground set. We obtain a new classification of closure matroids. Moreover, necessary and sufficient conditions for the direct sum, parallel extension connection and series extension connection to preserve k-balance property are given.

Item Type:Journal
Keywords:Amalgam, Balance, K-density, Graph, Matroid, Closure matroid
Subjects:Q Science, Computer Science
ID Code:5747

[1] T.A. Al-Hawary, Characterization of certain Matroids via Flats, Automata, Languages and Combinatorics, 7(3)(2002), 295-301.

[2] T.A. Al-Hawary, Characterizations of Matroids via OFR-sets, Turkish J. Math., 25(3)(2001), 445-455, .

[3] T.A. Al-Hawary, Feeble-Matroids, Italian J. Pure Appl. Math., 14(2003), 87-94.

[4] T.A. Al-Hawary, On balanced graphs and balanced matroids, Math. Sci. Res. Hot-Line 4 (7)(2000), 35-45.

[5] T.A. Al-Hawary, On k-balanced matroids, Mu’tah Lil-Buhuth wad-dirasat-Natural and applied sciences series 16(1) (2001), 15-22.

[6] T.A. Al-Hawary & J. McNulty, Closure Matroids, Cogressus Numerantium, 148, (2001), 93-95.

[7] J. Corp & J. McNulty, On a characterization of balanced matroids, Submitted.

[8] J. Corp & J. McNulty, On amalgams and density of uniform matroids, Congressus Numerantium 136 (1999), 193-199.

[9] H. Narayanan & M.N. Vartak, On molecular and atomic matroids, in Lecture Notes in Math, Calcutta, 1980 885 pp. 358-364, Springer, New York, 1981.

[10] J.G. Oxley, Matroid Theory, Oxford University Press, Oxford, 1992.

[11] N. White, ed., Theory of Matroids, Cambridge University Press, New York, 1986.

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