### Ascending subgraph decomposition

Combinatorics Seminar

6th December 2022, 11:00 am – 12:00 pm

Fry Building, 2.04

A conjecture of Alavi--Boals--Chartrand--Erdős--Oellermann (1987) asserts that every graph on (m+1 choose 2) edges can be decomposed into graphs G_1,...,G_m, where G_i has exactly i edges and is isomorphic to a subgraph of G_{i+1}; such a decomposition is called an ascending subgraph decomposition. We prove the conjecture for all large enough m.

This is joint work with Kyriakos Katsamaktsis, Alexey Pokrovskiy and Benny Sudakov.

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