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Smallest maximal matchings in the graph of the d-dimensional cube

✍ Scribed by Rodney Forcade


Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
213 KB
Volume
14
Category
Article
ISSN
0095-8956

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πŸ“œ SIMILAR VOLUMES


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We determine the maximum on n vertices can have, and we a question of Wilf. number of maximal independent sets which a connected graph completely characterize the extremal graphs, thereby answering \* Partially supported by NSF grant number DIMS-8401281. t Partially supported by NSF grant number D S

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Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,

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## Abstract We consider the problem of the minimum number of Hamiltonian cycles that could be present in a Hamiltonian maximal planar graph on __p__ vertices. In particular, we construct a __p__‐vertex maximal planar graph containing exactly four Hamiltonian cycles for every __p__ β‰₯ 12. We also pro

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## Abstract A maximal independent set of a graph __G__ is an independent set that is not contained properly in any other independent set of __G__. Let __i(G)__ denote the number of maximal independent sets of __G__. Here, we prove two conjectures, suggested by P. ErdΓΆs, that the maximum number of m

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## Abstract Let __p__ and __C__~4~ (__G__) be the number of vertices and the number of 4‐cycles of a maximal planar graph __G__, respectively. Hakimi and Schmeichel characterized those graphs __G__ for which __C__~4~ (__G__) = 1/2(__p__^2^ + 3__p__ ‐ 22). This characterization is correct if __p__ β‰₯

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✍ S. L. Hakimi; E. F. Schmeichel πŸ“‚ Article πŸ“… 1979 πŸ› John Wiley and Sons 🌐 English βš– 723 KB

Let G be a maximal planar graph with p vertices, and let Ck(G) denote the number of cycles of length k in G. We first present tight bounds for C,(G) and C,(G) in terms of p. We then give bounds for Ck(G) when 5 5 k 5 p , and consider in particular bounds for C,(G), in terms of p. Some conjectures an