m at h . C O ] 1 9 D ec 2 00 8 FINITE PLANAR EMULATORS FOR K 4 , 5 − 4 K
نویسنده
چکیده
In 1988 M. 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 K4,5 − 4K2. D. Archdeacon [2] showed that K4,5 − 4K2 does not admit a finite planar cover; thus K4,5 − 4K2 provides a counterexample to Fellows’ Conjecture. It is known that S. Negami’s Planar Cover Conjecture is true if and only if K1,2,2,2 admits no finite planar cover. We construct a finite planar emulator for K1,2,2,2. The existence of a finite planar cover for K1,2,2,2 is still open.
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