Two conjectures of Ringel

Abstract: In a graph decomposition problem, the goal is to partition the edge set of a host graph into a given set of pieces. I will focus on the setting where both the host graph and the pieces have a comparable number of vertices, and in particular on two conjectures of Ringel from the 60s on decomposing the complete graph: in the first (the generalised Oberwolfach problem) the pieces are 2-regular graphs, and in the second they are half-sized trees. I will give some ideas from my recent proofs of these problems for large graphs in joint work with Peter Keevash. The second conjecture was proved independently by Montgomery, Pokrovskiy and Sudakov.

discrete mathematicscombinatoricsprobability

Audience: researchers in the discipline

Australasian Combinatorics Seminar

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