Vol. 7, No. 6, 2014

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Seating rearrangements on arbitrary graphs

Daryl DeFord

Vol. 7 (2014), No. 6, 787–805

We exhibit a combinatorial model based on seating rearrangements, motivated by some problems proposed in the 1990s by Kennedy, Cooper, and Honsberger. We provide a simpler interpretation of their results on rectangular grids, and then generalize the model to arbitrary graphs. This generalization allows us to pose a variety of well-motivated counting problems on other frequently studied families of graphs.

matrix permanents, cycle covers, tilings, recurrence relations
Mathematical Subject Classification 2010
Primary: 05C30
Received: 4 November 2013
Revised: 3 January 2014
Accepted: 24 January 2014
Published: 20 October 2014

Communicated by Kenneth S. Berenhaut
Daryl DeFord
Department of Mathematics
Dartmouth College
27 North Main Street
Hanover, NH 03755
United States