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math.CO2025
Extending Thomassen's conjecture to directed graphs
Micha Christoph, Barnabás Janzer, Kalina Petrova +1
A famous conjecture by Thomassen from 1983 asserts that for any given there exists some such that every graph of minimum degree at leas…
math.CO2025
Critical edge sets in vertex-critical graphs
Ema Skottova, Raphael Steiner
Criticality is a fundamental notion in graph theory that has been studied continually since its introduction in the early 50s by Dirac. A graph is called -vertex-critical (-e…
math.CO2025
Proof of the KAMAK tree conjecture
Micha Christoph, Raphael Steiner
There are many intriguing questions in extremal graph theory that are well-understood in the undirected setting and yet remain elusive for digraphs. A natural instance of such a pr…