Packing and covering constants for certain families of trees. II

Meir, A.; Moon, J. W.

doi:10.1090/S0002-9947-1977-0460161-7

Packing and covering constants for certain families of trees. II
HTML articles powered by AMS MathViewer

by A. Meir and J. W. Moon

Trans. Amer. Math. Soc. 233 (1977), 167-178

DOI: https://doi.org/10.1090/S0002-9947-1977-0460161-7

PDF | Request permission

Abstract:

In an earlier paper we considered the problem of determining the packing and covering constants for families of trees whose generating function y satisfied a relation $y = x\phi (y)$ for some power series $\phi$ in y. In the present paper we consider the problem for some families of trees whose generating functions satisfy a more complicated relation.

References

Frank Harary and Edgar M. Palmer, Graphical enumeration, Academic Press, New York-London, 1973. MR 0357214
A. Meir and J. W. Moon, The expected node-independence number of random trees, Nederl. Akad. Wetensch. Proc. Ser. A 76=Indag. Math. 35 (1973), 335–341. MR 0345877, DOI 10.1016/1385-7258(73)90029-2
A. Meir and J. W. Moon, The expected node-independence number of various types of trees, Recent advances in graph theory (Proc. Second Czechoslovak Sympos., Prague, 1974) Academia, Prague, 1975, pp. 351–363. MR 0401520
A. Meir and J. W. Moon, Relations between packing and covering numbers of a tree, Pacific J. Math. 61 (1975), no. 1, 225–233. MR 401519, DOI 10.2140/pjm.1975.61.225
A. Meir and J. W. Moon, Packing and covering constants for certain families of trees. I, J. Graph Theory 1 (1977), no. 2, 157–174. Special issue dedicated to Paul Turán. MR 463001, DOI 10.1002/jgt.3190010211
J. W. Moon, Counting labelled trees, Canadian Mathematical Monographs, No. 1, Canadian Mathematical Congress, Montreal, Que., 1970. From lectures delivered to the Twelfth Biennial Seminar of the Canadian Mathematical Congress (Vancouver, 1969). MR 0274333
Richard Otter, The number of trees, Ann. of Math. (2) 49 (1948), 583–599. MR 25715, DOI 10.2307/1969046