id: 06000765
dt: j
an: 06000765
au: Derka, Martin
ti: Towards finite characterization of planar-emulable non-projective graphs.
so: Congr. Numerantium 207, 33-68 (2011).
py: 2011
pu: Utilitas Mathematica Publishing Inc., Winnipeg
la: EN
cc: 
ut: finite planar emulators for graphs; Negami’s conjecture
ci: 
li: 
ab: Summary: This paper deals with the problem of existence of finite planar
    emulators for graphs which do not have finite planar covers (cf.
    Negami’s conjecture). In [Encoding graphs in graphs, Ph.D.
    Dissertation, Univ. of California, San Diego (1985)], {\it M. Fellows}
    conjectured that such graphs do not exist. His conjecture was believed
    to be true for more than 20 years when it was surprisingly disproved at
    the end of 2008. In this paper, we study the class of the
    non-projective graphs with finite planar emulatorrs. We show that the
    graphs in this class must be planar expansions of internally
    4-connected graphs from a specific finite set, or contain one of six
    minor minimal non-projective graphs as a minor. We list this set and
    provide suggestions for a direction of future work in this field.
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