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University of Regina Department of Mathematics and Statistics

University of Regina
Department of Mathematics and Statistics
Speaker: Andrea Burgess (University of Ottawa)
Title: Cycle decompositions of some families of graphs
Time & Place: Friday, November 13, 3:30 - 4:30 pm, CL 435
A graph G is said to be decomposable into cycles of length k if its edges
may be partitioned into k-cycles. The study of cycle decomposition of the
complete graph Km dates back to the 19th century, when Kirkman proved
that Km decomposes into cycles of length 3 if and only if m is congruent to
1 or 3 modulo 6, and Walecki showed that Km is decomposable into cycles
of length m exactly when m is odd. The general problem of determining
necessary and sufficient conditions for the existence of a k-cycle decompo-
sition of Km remained open until recently; the final proof appeared in two
parts, by Alspach and Gavlas in 2001 when k is odd, and by Sajna in 2002
when k is even.
The study of cycle decompositions of complete graphs has been extended
to related families of graphs, including complete multigraphs and complete
equipartite graphs. Both of these families may be viewed as generaliza-


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics