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math.CO2025
Relative Turán densities for ordered graphs: all and nothing
Freddie Illingworth, Arjun Ranganathan, Leo Versteegen +1
Reiher, Rödl, Sales, and Schacht initiated the study of relative Turán densities of ordered graphs and showed that it is more subtle and interesting than the unordered case. For an…
math.CO2025
Treedepth and 2-treedepth in graphs with no long induced paths
Jędrzej Hodor, Freddie Illingworth, Tomasz Mazur
Huynh, Joret, Micek, Seweryn, and Wollan (Combinatorica, 2022) introduced a graph parameter, later referred to as 2-treedepth and denoted . The parameter is t…