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It has been established that the role played by complete graphs in graph theory is similar to the role Dowling group geometries and Projective geometries play in matroid theory. In this paper, we introduce a notion of H-tree, a class of representable matroids which play a similar role to trees in graph theory. Then we give some properties of H-trees such that when q = 0, then the results reduce to the known properties of trees in graph theory. Finally we give explicit expressions of the characteristic polynomials of H-trees, H-cycles, H-fans and H-wheels.
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참고문헌 (8)
참고문헌 신청
D. J. A. Welsh / 1969 / Euler and bipartite matroids / J. Combin. Theory 6 (4) : 375 ~ 377
E. G. Mphako / 2004 / H-lifts of tangential k-blocks / Discrete Math 285 (1-3) : 201 ~ 210
G. P. Whittle / 1989 / q-lifts of tangential k-blocks / J. London Math. Soc. (2) 39 (1) : 9 ~ 15
H. H. Crapo / 1969 / The Tutte polynomial / Aequationes Math 3 : 211 ~ 229
J. G. Oxley / 1992 / Matroid Theory / Oxford University Press
E. G. Mphako / 2004 / H-lifts of tangential k-blocks / Discrete Math 285 (1-3) : 201 ~ 210
G. P. Whittle / 1989 / q-lifts of tangential k-blocks / J. London Math. Soc. (2) 39 (1) : 9 ~ 15
H. H. Crapo / 1969 / The Tutte polynomial / Aequationes Math 3 : 211 ~ 229
J. G. Oxley / 1992 / Matroid Theory / Oxford University Press
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