Combinatorial Mathematics: Proceedings of the International by J. A. Bondy (auth.), D. A. Holton, Jennifer Seberry (eds.) PDF

By J. A. Bondy (auth.), D. A. Holton, Jennifer Seberry (eds.)

ISBN-10: 3540089535

ISBN-13: 9783540089537

ISBN-10: 3540357025

ISBN-13: 9783540357025

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Extra resources for Combinatorial Mathematics: Proceedings of the International Conference on Combinatorial Theory Canberra, August 16–27, 1977

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05C99 ISOMORPHIC FACTORISATIONS III: Frank Harary Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, UNITED STATES OF AMERICA COMPLETE MULTIPARTITE GRAPHS Robert W. Robinson and Nicholas C. Wormald Department of Mathematics, University of Newcastle, New South Wales, 2308, AUSTRALIA ABSTRACT In the first paper of this series we showed that a factorisation of the complete graph K into t isomorphic subgraphs exists whenever the Divisibility P Condition holds, that is, the number of lines is divisible by t.

1969. Isomorphic Factorisations I: Complete graphs, Trans. Amer. Math. , to appear. 3. F. D. Wallis, Isomorphic factorisations II: Combinatorial designs, Proceedings of the Eighth Southeastern Conference on Oombinatorics, Graph Theory and Computing, 4. S. Yamamoto, H. Ikeda, S. Shige-eda, decomposition 5 (1975) Utilitas Math. , Winnipeg, K. Ushio and N. Hamada, of complete graphs and complete bigraphs, 33-42. to appear. On claw- Hiroshima Math. J. 05B05, 05B25, 05B30 BIPLANES AND S~4I-BIPLANES D a n i e l Hughes W e s t f i e l d College (University of London) L o n d o n NW3 7ST i.

As A 1 u B2, BI, A 2 u B 4 and B 3 all have cardinality GI,G2,G 3 and G 4 are all isomorphic Note Let A = A 1 u A 2 and B = Then A has cardinality m, B has cardinality Let G 1 be the spanning subgraph of K{A,B,C) spanning subgraphs (b+a)/2 s points. to K(a,b) u K((a+b)/2,s). (a+b)/2, clearly Hence the latter graph is in K(m,n,s)/~. The graphs GI,G2,G 3 and G 4 are illustrated conventions as in Figure i, in Figure 2 following the same Note that by combining G 1 and G 3 into the one graph, we obtain the element of K(m~,~/2 which was constructed in the proof of Theorem 2.

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Combinatorial Mathematics: Proceedings of the International Conference on Combinatorial Theory Canberra, August 16–27, 1977 by J. A. Bondy (auth.), D. A. Holton, Jennifer Seberry (eds.)


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