Nonexistence of a Weakly Neighbourly Polyhedral Map of Type {6, 6}
Nilakantan, Nandini
Experiment. Math., Tome 12 (2003) no. 1, p. 257-262 / Harvested from Project Euclid
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For the existence of an n-vertex polyhedral map of type {p, p}, it is known that n must be {\small $\geq (p-1)^2$} and equality holds if and only if K is weakly neighbourly. In 2002, Brehm et al. saw that there is a unique polyhedral map of type {\small $\{5, 5\}$} on 16 vertices. In 1990, Brehm constructed a polyhedral map of type {\small $\{6, 6\}$} with 26 vertices. In this article, we prove that there do not exist any polyhedral maps of type {\small $\{6, 6\}$} on 25 vertices. As a consequence, we show that the minimum number of edges in polyhedral maps of Euler characteristic -25 is {\small $>$} 75.
Publié le : 2003-05-14
Classification:  Polyhedral maps,  polyhedral 2-manifolds,  regular graph design,  52B70,  51M20,  57M20 
@article{1087329229,
     author = {Nilakantan, Nandini},
     title = {Nonexistence of a Weakly Neighbourly Polyhedral Map of Type {6, 6}},
     journal = {Experiment. Math.},
     volume = {12},
     number = {1},
     year = {2003},
     pages = { 257-262},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087329229}
}

Nilakantan, Nandini. Nonexistence of a Weakly Neighbourly Polyhedral Map of Type {6, 6}. Experiment. Math., Tome 12 (2003) no. 1, pp.  257-262. http://gdmltest.u-ga.fr/item/1087329229/