Nonrepetitive Colouring via Entropy Compression

A vertex colouring of a graph is \emph{nonrepetitive} if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively $k$-choosable if given lists of at least $k$ colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that every graph with maximum degree $\Delta$ is $c\Delta^2$-choosable, for some constant $c$. We prove this result with $c=1$ (ignoring lower order terms). We then prove that every subdivision of a graph with sufficiently many division vertices per edge is nonrepetitively 5-choosable. The proofs of both these results are based on the Moser-Tardos entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek for the nonrepetitive choosability of paths. Finally, we prove that every graph with pathwidth $k$ is nonrepetitively $O(k^{2})$-colourable.Comment: v4: Minor changes made following helpful comments by the referee

Epidemiological, genetic, and clinical characterization by age of newly diagnosed acute myeloid leukemia based on an academic population-based registry study (AMLSG BiO)

We describe genetic and clinical characteristics of acute myeloid leukemia (AML) patients according to age from an academic population-based registry. Adult patients with newly diagnosed AML at 63 centers in Germany and Austria were followed within the AMLSG BiO registry (NCT01252485). Between January 1, 2012, and December 31, 2014, data of 3525 patients with AML (45% women) were collected. The median age was 65 years (range 18–94). The comparison of age-specific AML incidence rates with epidemiological cancer registries revealed excellent coverage in patients 0 were associated with non-intensive treatment or best supportive care. The AMLSG BiO registry provides reliable population-based distributions of genetic, clinical, and treatment characteristics according to age

Nonrepetitive edge-colorings of trees

A repetition is a sequence of symbols in which the first half is the same asthe second half. An edge-coloring of a graph is repetition-free ornonrepetitive if there is no path with a color pattern that is a repetition.The minimum number of colors so that a graph has a nonrepetitive edge-coloringis called its Thue edge-chromatic number. We improve on the best known general upper bound of $4\Delta-4$ for the Thueedge-chromatic number of trees of maximum degree $\Delta$ due to Alon,Grytczuk, Ha{\l}uszczak and Riordan (2002) by providing a simple nonrepetitiveedge-coloring with $3\Delta-2$ colors

Extremal problems for chromatic neighborhood sets

“This is a preprint of an article accepted for publication in [Journal of Graph Theory]  copyright (2002) Wiley Periodicals,Inc.The chromatic neighborhood sequence of a graph G is the list of the chromatic numbers of the subgraphs induced by the neighborhoods of the vertices. We study the maximum multiplicity of this sequence, proving, amongst other things, that if a chromatic neighborhood sequence has t distinct values, the largest value being dt, then there is a value with multiplicity at least (unable to display equation). This bound is asymptotically tigh

Nonrepetitive edge-colorings of trees

A repetition is a sequence of symbols in which the first half is the same as the second half. An edge-coloring of a graph is repetition-free or nonrepetitive if there is no path with a color pattern that is a repetition. The minimum number of colors so that a graph has a nonrepetitive edge-coloring is called its Thue edge-chromatic number. We improve on the best known general upper bound of $4\Delta-4$ for the Thue edge-chromatic number of trees of maximum degree $\Delta$ due to Alon, Grytczuk, Ha{\l}uszczak and Riordan (2002) by providing a simple nonrepetitive edge-coloring with $3\Delta-2$ colors

Analysis of the impact of adherence to guidelines and expert advice in patients with myelodysplastic syndromes.

The European Leukemia Net (ELN) guidelines for treatment of myelodysplastic syndromes (MDS) connect heterogeneous MDS subgroups with a number of therapeutic options ranging from best supportive care to allogeneic stem cell transplantation (alloSCT). However, it is currently unknown whether adherence to guideline recommendations translates into improved survival. The sizeable database of the Duesseldorf MDS Registry allowed us to address this question. We first performed a retrospective analysis including 1698 patients (cohort 1) to whom we retrospectively applied the ELN guidelines. We compared patients treated according to the guidelines with patients who deviated from it, either because they received a certain treatment though it was not recommended or because they did not receive that treatment despite being eligible. We also performed a prospective study with 381 patients (cohort 2) who were seen in our department and received guideline-based expert advice. Again, we compared the impact of subsequent guideline-adherent versus non-adherent treatment. For the majority of treatment options (best supportive care, lenalidomide, hypomethylating agents, low-dose chemotherapy, and intensive chemotherapy), we found that adherence to the ELN guidelines did not improve survival in cohort 1. The same was true when patient management was prospectively enhanced through guideline-based treatment advice given by MDS experts (cohort 2). The only exceptions were alloSCT and iron chelation (ICT). Patients receiving ICT and alloSCT as recommended fared significantly better than those who were eligible but received other treatment. Our analysis underscores the limited survival impact of most MDS therapies and suggests to pursue alloSCT in all suitable candidates. Graphical abstract