Dense flag triangulations of 3-manifolds via extremal graph theory

We characterize f-vectors of sufficiently large three-dimensional flag Gorenstein* complexes, essentially confirming a conjecture of Gal [Discrete Comput. Geom., 34 (2), 269--284, 2005]. In particular, this characterizes f-vectors of large flag triangulations of the 3-sphere. Actually, our main result is more general and describes the structure of closed flag 3-manifolds which have many edges. Looking at the 1-skeleta of these manifolds we reduce the problem to a certain question in extremal graph theory. We then resolve this question by employing the Supersaturation Theorem of Erdos and Simonovits.Comment: Trans. AMS, to appea

Chromatic roots and limits of dense graphs

In this short note we observe that recent results of Abert and Hubai and of Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic moments of the roots of the chromatic polynomial extend to the theory of dense graph sequences. We offer a number of problems and conjectures motivated by this observation.Comment: 9 page

Note on bipartite graph tilings

Let s<t be two fixed positive integers. We study what are the minimum degree conditions for a bipartite graph G, with both color classes of size n=k(s+t), which ensure that G has a K_{s,t}-factor. Exact result for large n is given. Our result extends the work of Zhao, who determined the minimum degree threshold which guarantees that a bipartite graph has a K_{s,s}-factor.Comment: 6 pages, no figures; statement of the main theorem corrected (thanks to Andrzej Czygrinow and Louis DeBiasio); to appear in SIAM Journal on Discrete Mathematic

The approximate Loebl-Komlos-Sos conjecture and embedding trees in sparse graphs

Loebl, Koml\'os and S\'os conjectured that every $n$-vertex graph $G$ with at least $n/2$ vertices of degree at least $k$ contains each tree $T$ of order $k+1$ as a subgraph. We give a sketch of a proof of the approximate version of this conjecture for large values of $k$. For our proof, we use a structural decomposition which can be seen as an analogue of Szemer\'edi's regularity lemma for possibly very sparse graphs. With this tool, each graph can be decomposed into four parts: a set of vertices of huge degree, regular pairs (in the sense of the regularity lemma), and two other objects each exhibiting certain expansion properties. We then exploit the properties of each of the parts of $G$ to embed a given tree $T$. The purpose of this note is to highlight the key steps of our proof. Details can be found in [arXiv:1211.3050]

Artistic impressions from the Conference and Vienna city

Several drawings during the European Physical Society Conference on High Energy Physics (22–29 July 2015) activity are performed and presented here together with the drawings from Vienna city made in last few years. Also the Higgs boson, seen by the eye of the artist, is presented here by the sculpture from glass and metals. The autor will illustrate the connection of the science and arts. Both „drink the water from the see of phantasy, which helps them to come to finest ideas.“ One helps to other and together bring better understanding in human society

Combination of D∗+−D^{*+-} Differential Cross-Section Measurements in Deep-Inelastic ep\it ep Scattering at HERA

H1 and ZEUS have published single differential cross sections for inclusive D*±-meson production in deep-inelastic electron-proton scattering at HERA from their respective final data sets. The cross sections are here combined in common visible phase space region of photon virtuality Q² > 5 GeV2, electron inelasticity 0.02 1.5 GeV and pseudorapidity |η(D*±)| 1.5 GeV2 .Perturbative next-to-leading-order QCD predictions are compared with the experimental results obtained

Artistic impressions from the Conference and Vienna city

Several drawings during the European Physical Society Conference on High Energy Physics (22–29 July 2015) activity are performed and presented here together with the drawings from Vienna city made in last few years. Also the Higgs boson, seen by the eye of the artist, is presented here by the sculpture from glass and metals. The autor will illustrate the connection of the science and arts. Both „drink the water from the see of phantasy, which helps them to come to finest ideas.“ One helps to other and together bring better understanding in human society