Finite planar emulators for K_{4,5} - 4K_2 and K_{1,2,2,2} and Fellows' Conjecture
Combinatorics
2012-04-10 v3
Abstract
In 1988 Fellows conjectured that if a finite, connected graph admits a finite planar emulator, then it admits a finite planar cover. We construct a finite planar emulator for K_{4,5} - 4K_2. Archdeacon showed that K_{4,5} - 4K_2 does not admit a finite planar cover; thus K_{4,5} - 4K_2 provides a counterexample to Fellows' Conjecture. It is known that Negami's Planar Cover Conjecture is true if and only if K_{1,2,2,2} admits no finite planar cover. We construct a finite planar emulator for K_{1,2,2,2}. The existence of a finite planar cover for K_{1,2,2,2} is still open.
Cite
@article{arxiv.0812.3700,
title = {Finite planar emulators for K_{4,5} - 4K_2 and K_{1,2,2,2} and Fellows' Conjecture},
author = {Yo'av Rieck and Yasushi Yamashita},
journal= {arXiv preprint arXiv:0812.3700},
year = {2012}
}
Comments
Final version. To appear in European Journal of Combinatorics