Professor Dean Hoffman, Auburn University, (Raybould Fellow) will give 
three seminars as follows:

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(1) Friday 9th July, 11am in room 67-343

    "A problem of mixed differences, kinda, sorta..."

Abstract.
Difference methods have suggested all kinds of interesting problems in
the integers (mod) n, or more generally, over a group of permutations of
a finite set. We present one that at least we can solve over the
integers.

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(2) Tuesday 13th July, 11am in room 67-343

    "The Grundy colouring number of the n-cube"

Abstract.
Each linear ordering of the vertices of a graph determines the following
proper coloring of the graph with colors 0, 1, 2, ... : color the
vertices in the order given, at each stage using the smallest allowed
color. The maximum, over all orderings, of the number of colors used is
defined to be the Grundy coloring number of the graph. We determine this
parameter for the n-cube, using Hamming codes. (Joint with P.D. Johnson)

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(3) Friday 16th July, 11am in room 67-343

    "An f-factor theorem for signed graphs"

Abstract.
A signed graph is a graph with two kinds of edges, positive edges and 
negative edges. The degree of a vertex in in a signed graph is the
number of positive edge ends there minus the number of negative edge
ends there. We prove a version of Tutte's f-factor theorem for these
graphs, and use it to characterize degree sequences of simple signed
graphs. (Joint with H. Gavlas)

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