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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…
Cycle-factors of regular graphs via entropy
Micha Christoph, Nemanja Draganić, António Girão +3
It is a classical result that a random permutation of elements has, on average, about cycles. We generalise this fact to all directed -regular graphs on vertice…
On a Ramsey--Turán variant of Roth's theorem
Matija Bucić, Micha Christoph, Jaehoon Kim +2
A classical theorem of Roth states that the maximum size of a solution-free set of a homogeneous linear equation in is if and only if the sum of…
New bounds for linear arboricity and related problems
Micha Christoph, Nemanja Draganić, António Girão +3
A linear forest is a collection of vertex-disjoint paths. The Linear Arboricity Conjecture states that every graph of maximum degree can be decomposed into at most $\lceil(Δ+1)…
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…
Universality for transversal Hamilton cycles in random graphs
Micha Christoph, Anders Martinsson, Aleksa Milojević
A tuple of graphs on the same vertex set of size is said to be Hamilton-universal if for every map there exists a Hamilton cycle whose -th e…
Almost-perfect colorful matchings in three-edge-colored bipartite graphs
Simona Boyadzhiyska, Micha Christoph, Tibor Szabó
We prove that, for positive integers satisfying , it holds that any bipartite graph which is the union of three perfect matchings , $M…