# New PDF release: Combinatorics 79 Part I

By M. Deza and I.G. Rosenberg (Eds.)

ISBN-10: 0444861106

ISBN-13: 9780444861108

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Additional info for Combinatorics 79 Part I

Example text

E. if P is connected, d ( P ) > 1 and a ( P ) = 2 d ‘ P ’ + ’ - 2 . If Q is a connected minor of a connected matroid perspective P there exists a sequence of connected matroid perspectives Po = P, P 1 ,. . ,Pk = Q such that Pi+1 is obtained from Pi by deleting or contracting one element for i = 0, 1, . . 81). 5. Any connected minor of degree >1 of an a-minimal matroid perspective is also a-minimal. 5 there is a characterization by excluded minors of a-minimal matroid perspectives. The list of excluded minors is infinite: for all n 3 3 (ff :-I, ‘5L) is not a-minimal but every proper minor is.

Theory 5 (1968) 185-191. [16] M. R. Acad. Sci. Paris (A) 280 (1975) 61-64. [17] M. Las Vergnas, Convexity in oriented matroids, J. Combin. Theory (B) 29 (1980) 231-243. [IS] M. R. Acad. Sci. Paris (A) 280 (1975) 1479-1482. [19] M. Las Vergnas, Coordinatizable strong maps of matroids, J. Combin. Theory (B), to appear. Cf. p. 441 in Problemes combinatoires et ThCorie des Graphes, Proc. , Paris, 1978). [20] M. Las Vergnas, Acyclic and totally cyclic orientations of combinatorial geometries, Discrete Math.

Stanley, Acyclic orientations of graphs, Discrete Math. 5 (1973) 171-178. T. Tutte, A ring in Graph Theory, Proc. Cambridge Philos. 43 (1947) 26-40. T. Tutte, A contribution to the theory of chromatic polynomials, Can. J. Math. 6 (1954) 80-91. T. Tutte, The dichromatic polynomial, in: Proc. , Winnipeg, 1976) 605-635. A. Welsh, Matroid Theory (Academic Press, London, 1976). [36] H. Whitney, A logical expansion in mathematics, Bull. Am. Math. 38 (1932) 572-579. [37] H. Whitney, The coloring of graphs, Ann.