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SUMMARY:On Graphs Defined by Some Systems of Equations - Felix Lazebnik (U
 niversity of Delaware)
DTSTART:20141023T133000Z
DTEND:20141023T143000Z
UID:TALK54120@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:In this talk I will present a simple method for constructing i
 nfinite families of graphs defined by a class of systems of equations over
  commutative rings.  The graphs in all such families possess some general\
 nproperties including regularity or bi-regularity\, existence of special v
 ertex colorings\, and existence of covering maps between every two members
  of the same family (hence\, embedded spectra). Another general property i
 s that nearly every graph constructed in this manner edge-decomposes eithe
 r the complete\, or complete bipartite\, graph which it spans.\n\nIn many 
 instances\, specializations of these constructions have proved useful in v
 arious graph theory problems\, but especially in many extremal problems wh
 ich deal with cycles in graphs. I will explain motivations for these const
 ructions\, survey both old and new results\, and state open questions.\n
LOCATION:MR12
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