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
Smallest maximal matchings in the graph of the d-dimensional cube
β Scribed by Rodney Forcade
- Publisher
- Elsevier Science
- Year
- 1973
- Tongue
- English
- Weight
- 213 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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,
## 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__βvertex maximal planar graph containing exactly four Hamiltonian cycles for every __p__ β₯ 12. We also pro
## 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
## Abstract Let __p__ and __C__~4~ (__G__) be the number of vertices and the number of 4βcycles 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__ β 22). This characterization is correct if __p__ β₯
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