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                Department of Mathematical Sciences                       
                   The Johns Hopkins University                           
                                                                        
                              SEMINAR                                
                                                                        
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Professor Daniel Ullman                           February 24, 2000
Department of Mathematics                         304 Whitehead Hall
The George Washington University                  Preseminar: 3:00 p.m.
                                                  Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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         GIRTH AND FRACTIONAL CHROMATIC NUMBER OF PLANAR GRAPHS

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                             ABSTRACT

In 1959, even before the Four Color Theorem was proved, Grotzsch showed
that planar graphs with girth at least 4 have chromatic number at
most 3.  We examine the fractional analogue of this theorem and its
generalizations.  For any fixed girth, we ask for the largest possible
fractional chromatic number of a planar graph with that girth, and we
provide upper and lower bounds for this quantity.

(This is joint work with Amir Pirnazar.)

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