On bounding the difference between the maximum degree and the chromatic number by a constant

We provide a finite forbidden induced subgraph characterization for the graph class $\varUpsilon_k$, for all $k \in \mathbb{N}_0$, which is defined as follows. A graph is in $\varUpsilon_k$ if for any induced subgraph, $\Delta \leq \chi -1 + k$ holds, where $\Delta$ is the maximum degree and $\chi$ is the chromatic number of the subgraph. We compare these results with those given in [O. Schaudt, V. Weil, On bounding the difference between the maximum degree and the clique number, Graphs and Combinatorics 31(5), 1689-1702 (2015). DOI: 10.1007/s00373-014-1468-3], where we studied the graph class $\varOmega_k$, for $k \in \mathbb{N}_0$, whose graphs are such that for any induced subgraph, $\Delta \leq \omega -1 + k$ holds, where $\omega$ denotes the clique number of a graph. In particular, we give a characterization in terms of $\varOmega_k$ and $\varUpsilon_k$ of those graphs where the neighborhood of every vertex is perfect.Comment: 10 pages, 4 figure

On bounding the difference of the maximum degree and clique number

For every k ∈ ℕ0, we consider graphs in which for any induced subgraph, Δ ≤ ω−1+k holds, where Δ is the maximum degree and ω is the maximum clique number of the subgraph. We give a finite forbidden induced subgraph characterization for every k. As an application, we find some results on the chromatic number χ of a graph. B.Reed stated the conjecture that for every graph, χ ≤ ⌈Δ+ω+1 / 2⌉ holds. Since this inequality is fulfilled by graphs in which Δ ≤ ω+2 holds, our results provide a hereditary graph class for which the conjecture holds

On the separability of graphs

Recently, Cicalese and Milanič introduced a graph-theoretic concept called separability. A graph is said to be k-separable if any two non-adjacent vertices can be separated by the removal of at most k vertices. The separability of a graph G is the least k for which G is k-separable. In this paper, we investigate this concept under the following three aspects. First, we characterize the graphs for which in any non-complete connected induced subgraph the connectivity equals the separability, so-called separability-perfect graphs. We list the minimal forbidden induced subgraphs of this condition and derive a complete description of the separability-perfect graphs.We then turn our attention to graphs for which the separability is given locally by the maximum intersection of the neighborhoods of any two non-adjacent vertices. We prove that all (house,hole)-free graphs fulfill this property – a class properly including the chordal graphs and the distance-hereditary graphs. We conclude that the separability can be computed in O(m∆) time for such graphs.In the last part we introduce the concept of edge-separability, in analogy to edge-connectivity, and prove that the class of k-edge-separable graphs is closed under topological minors for any k. We explicitly give the forbidden topological minors of the k-edge-separable graphs for each 0 ≤ k ≤ 3

On the separability of graphs

Recently, Cicalese and Milanič introduced a graph-theoretic concept called separability. A graph is said to be k-separable if any two non-adjacent vertices can be separated by the removal of at most k vertices. The separability of a graph G is the least k for which G is k-separable. In this paper, we investigate this concept under the following three aspects. First, we characterize the graphs for which in any non-complete connected induced subgraph the connectivity equals the separability, so-called separability-perfect graphs. We list the minimal forbidden induced subgraphs of this condition and derive a complete description of the separability-perfect graphs.We then turn our attention to graphs for which the separability is given locally by the maximum intersection of the neighborhoods of any two non-adjacent vertices. We prove that all (house,hole)-free graphs fulfill this property ? a class properly including the chordal graphs and the distance-hereditary graphs. We conclude that the separability can be computed in O(m?) time for such graphs.In the last part we introduce the concept of edge-separability, in analogy to edge-connectivity, and prove that the class of k-edge-separable graphs is closed under topological minors for any k. We explicitly give the forbidden topological minors of the k-edge-separable graphs for each 0 ≤ k ≤ 3

Struktur und Entwicklung des Oberrheingrabens als europäischer Wirtschaftsstandort - Kurzfassung

In dieser Arbeit wird die ökonomische Situation des Oberrheingrabens anhand der Themenbereiche Beschäftigung und Arbeitslosigkeit, Forschung und Entwicklung, Wachstum und Produktivität und Unternehmensgründungen analysiert. Zudem werden die wichtigsten infrastrukturellen Rahmenbedingungen, die Bevölkerungsentwicklung und Unterschiede in der Besteuerung und in den Genehmigungsverfahren innerhalb des trinationalen Oberrheingrabens dargestellt. Darauf aufbauend wird das Potential und die mögliche Rolle der Region als europäischer Wirtschaftsstandort diskutiert. Die Untersuchung entstand in Zusammenarbeit zwischen dem Institut für angewandte Wirtschaftsforschung, IAW, in Tübingen, der Konjunkturforschung Basel AG, BAK, in Basel und dem Zentrum für Europäische Wirtschaftsforschung, ZEW, in Mannheim. Dabei übernahm das IAW die Untersuchung der Bevölkerungsentwicklung, des Arbeitsmarktes, der Gewerbeflächen und des Wohnungsmarktes. Das BAK untersuchte das regionale Wachstum, die Produktivitätsentwicklung und die nationalen Genehmigungsverfahren. Die Kapitel über die Verkehrsinfrastruktur, die Besteuerung der Unternehmen, Forschung und Entwicklung und Unternehmensgründungen wurden vom ZEW erstellt. Die Schlußfolgerungen wurden gemeinsam von den drei Instituten erarbeitet

Struktur und Entwicklung des Oberrheingrabens als europäischer Wirtschaftsstandort: Zurzfassung

In dieser Arbeit wird die ökonomische Situation des Oberrheingrabens anhand der Themenbereiche Beschäftigung und Arbeitslosigkeit, Forschung und Entwicklung, Wachstum und Produktivität und Unternehmensgründungen analysiert. Zudem werden die wichtigsten infrastrukturellen Rahmenbedingungen, die Bevölkerungsentwicklung und Unterschiede in der Besteuerung und in den Genehmigungsverfahren innerhalb des trinationalen Oberrheingrabens dargestellt. Darauf aufbauend wird das Potential und die mögliche Rolle der Region als europäischer Wirtschaftsstandort diskutiert. Die Untersuchung entstand in Zusammenarbeit zwischen dem Institut für angewandte Wirtschaftsforschung, IAW, in Tübingen, der Konjunkturforschung Basel AG, BAK, in Basel und dem Zentrum für Europäische Wirtschaftsforschung, ZEW, in Mannheim. Dabei übernahm das IAW die Untersuchung der Bevölkerungsentwicklung, des Arbeitsmarktes, der Gewerbeflächen und des Wohnungsmarktes. Das BAK untersuchte das regionale Wachstum, die Produktivitätsentwicklung und die nationalen Genehmigungsverfahren. Die Kapitel über die Verkehrsinfrastruktur, die Besteuerung der Unternehmen, Forschung und Entwicklung und Unternehmensgründungen wurden vom ZEW erstellt. Die Schlußfolgerungen wurden gemeinsam von den drei Instituten erarbeitet. --

Prevention and Mitigation of Acute Radiation Syndrome in Mice by Synthetic Lipopeptide Agonists of Toll-Like Receptor 2 (TLR2)

Bacterial lipoproteins (BLP) induce innate immune responses in mammals by activating heterodimeric receptor complexes containing Toll-like receptor 2 (TLR2). TLR2 signaling results in nuclear factor-kappaB (NF-κB)-dependent upregulation of anti-apoptotic factors, anti-oxidants and cytokines, all of which have been implicated in radiation protection. Here we demonstrate that synthetic lipopeptides (sLP) that mimic the structure of naturally occurring mycoplasmal BLP significantly increase mouse survival following lethal total body irradiation (TBI) when administered between 48 hours before and 24 hours after irradiation. The TBI dose ranges against which sLP are effective indicate that sLP primarily impact the hematopoietic (HP) component of acute radiation syndrome. Indeed, sLP treatment accelerated recovery of bone marrow (BM) and spleen cellularity and ameliorated thrombocytopenia of irradiated mice. sLP did not improve survival of irradiated TLR2-knockout mice, confirming that sLP-mediated radioprotection requires TLR2. However, sLP was radioprotective in chimeric mice containing TLR2-null BM on a wild type background, indicating that radioprotection of the HP system by sLP is, at least in part, indirect and initiated in non-BM cells. sLP injection resulted in strong transient induction of multiple cytokines with known roles in hematopoiesis, including granulocyte colony-stimulating factor (G-CSF), keratinocyte chemoattractant (KC) and interleukin-6 (IL-6). sLP-induced cytokines, particularly G-CSF, are likely mediators of the radioprotective/mitigative activity of sLP. This study illustrates the strong potential of LP-based TLR2 agonists for anti-radiation prophylaxis and therapy in defense and medical scenarios

On Bounding the Difference of the Maximum Degree and the Clique Number

For every , we consider graphs in which for any induced subgraph, holds, where is the maximum degree and is the maximum clique number of the subgraph. We give a finite forbidden induced subgraph characterization for every . As an application, we find some results on the chromatic number of a graph. B. Reed stated the conjecture that for every graph, holds. Since this inequality is fulfilled by graphs in which holds, our results provide a hereditary graph class for which the conjecture holds