Abstract
Every graph having vertex degrees zero and two satisfying the basic necessary conditions is the leave of a maximal partial triple system, with one exception (C 4 ⋃C 5). The proof technique is direct, using the method of differences.
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References
Andersen, L.D., Hilton, A.J.W., Mendelsohn, E.: Embedding partial Steiner triple systems. Proc. London Math. Soc.41, 557–576 (1980)
Castagna, F., Prins, G.: Every generalized Petersen graph has a Tait coloring. Pacific J. Math.40, 53–58 (1972).
Colbourn, C.J.: Embedding partial Steiner triple systems is NP-complete. J. Comb. Theory (A)35, 100–105 (1983)
Colbourn, C.J., Colbourn, M.J., Rosa, A.: Completing small partial triple systems. Discrete Math.45, 165–179 (1983)
Colbourn, C.J., Jungnickel, D., Rosa, A.: The strong chromatic number of partial triple system. Discrete Appl. Math (to appear)
Colbourn, C.J., Rosa, A.: Maximal partial triple systems of orderv ≤ 11. Ars Comb.20, 5–28 (1985)
Colbourn, C.J., Rosa, A.: Element neighbourhoods in twofold triple systems. J. of Geom. (to appear)
Colbourn, M.J., Mathon, R.A.: On cyclic Steiner 2-designs. Ann. Discrete Math.7, 215–253 (1980)
Hartman, A.: Tripling quadruple systems. Ars Comb.10, 255–309 (1980)
Hilton, A.J.W., Rodger, C.A.: Triangulating nearly complete graphs of odd order (in preparation)
Mendelsohn, E.: private communications 1984
Novák, J.: Edge bases of complete uniform hypergraphs. Mat. Čas.24, 43–57 (1974)
Novák, J.: Přiśpěvek k teorii kombinaci. Čas. Pěstováni Mat.88, 129–141 (1963)
Simpson, J.E.: Langford sequences: perfect and hooked. Discrete Math.44, 97–104 (1983)
Spencer, J.: Maximal consistent families of triples. J. Comb. Theory5 1–8 (1968)
Stern, G., Lenz, H.: Steiner triple systems with given subspaces: another proof of the Doyen-Wilson theorem. Boll. Unione Mat. Ital. (A)17, 109–114 (1980)
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Colbourn, C.J., Rosa, A. Quadratic leaves of maximal partial triple systems. Graphs and Combinatorics 2, 317–337 (1986). https://doi.org/10.1007/BF01788106
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DOI: https://doi.org/10.1007/BF01788106