Finite planar emulators for K4,5-4K2 and K1,2,2,2 and Fellows' Conjecture

Authors:
Yo'av Rieck;Yasushi Yamashita
Affiliations:
Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, United States;Department of Information and Computer Sciences, Nara Women's University Kitauoya Nishimachi, Nara 630-8506, Japan
Venue:
European Journal of Combinatorics
Year:
2010

Citing 5
Cited 5

Projective planarity in linear time

Journal of Algorithms
Graph minors. XIII: the disjoint paths problem

Journal of Combinatorial Theory Series B
Graph Minors. XX. Wagner's conjecture

Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
A note on possible extensions of Negami's conjecture

Journal of Graph Theory
Two graphs without planar covers

Journal of Graph Theory

Computing role assignments of chordal graphs

Theoretical Computer Science
Computing role assignments of proper interval graphs in polynomial time

IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
How not to characterize planar-emulable graphs

IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Computing role assignments of proper interval graphs in polynomial time

Journal of Discrete Algorithms
Mike fellows: weaving the web of mathematics and adventure

The Multivariate Algorithmic Revolution and Beyond

Quantified Score

Hi-index	0.00

Visualization

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 [Dan Archdeacon, Two graphs without planar covers, J. Graph Theory, 41 (4) (2002) 318-326] 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.