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On a conjecture on maximal planar sequences

✍ Scribed by Stefano Fanelli

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
137 KB
Volume
4
Category
Article
ISSN
0364-9024

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✦ Synopsis

Let d$ d:2 * . $0 denote the nonincreasing sequence d,, . . . , d,, d,, . . . , d 2 , . . . , d,, . . . , dp, where the term d, appears kj times ( i = 1 . 2 , . . . , p ) . In this work the author proves that the maximal 2sequences: 7361515, 756' 5", 776' 5" are planar graphical, in contrast to a conjecture by Schmeichel and Hakimi.

πŸ“œ SIMILAR VOLUMES

An unresolved conjecture on nonmaximal p
An unresolved conjecture on nonmaximal planar graphical sequences
✍ Stefano Fanelli πŸ“‚ Article πŸ“… 1981 πŸ› Elsevier Science 🌐 English βš– 229 KB

In this work it is shown that the E&x nonmaxir:lal sequences, 5S555555555553 755555555555555555 (more briefly 5133' 7'5") are not pl-nar graphical, partly proving an unresolved conjecture by Schmeichel and Hakimi.

On the connectivity of maximal planar gr
On the connectivity of maximal planar graphs
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On possible counterexamples to Negami's
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## Abstract A simple graph **__H__** is a cover of a graph **__G__** if there exists a mapping Ο† from **__H__** onto **__G__** such that Ο† maps the neighbors of every vertex Ο… in **__H__** bijectively to the neighbors of Ο† (Ο…) in **__G__**. Negami conjectured in 1986 that a connected graph has a fi

On the number of hamiltonian cycles in a
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✍ S. L. Hakimi; E. F. Schmeichel; C. Thomassen πŸ“‚ Article πŸ“… 1979 πŸ› John Wiley and Sons 🌐 English βš– 243 KB πŸ‘ 2 views

## 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