The optimal pebbling number of staircase graphs

Let G be a graph with a distribution of pebbles on its vertices. A pebbling move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The optimal pebbling number of G is the smallest number of pebbles which can be placed on the vertices of G such that, for any vertex v of G, there is a sequence of pebbling moves resulting in at least one pebble on v. We determine the optimal pebbling number for several classes of induced subgraphs of the square grid, which we call staircase graphs. © 2018 Elsevier B.V

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

The Gifted and Gifted Education in Hungary

The real challenge is to see value that is not yet in its true form. Becoming gifted is a process, during which characteristics of giftedness are present throughout, but not necessarily in a form perceptible or acceptable to the environment. Giftedness does not hide itself, only to the extent that the environment believes it hidden. Perception defines the pattern that manifests itself. The beginning of the 20th century is a success story of Hungarian gifted education. Outstanding teachers and their students have reached outstanding achievements through gifted education linked to everyday education. Their methods and ideas are durable, and are therefore worth recalling

Hydrothermal dolomitization of basinal deposits controlled by a synsedimentary fault system in Triassic extensional setting, Hungary

Dolomitization of relatively thick carbonate successions occurs via an effective fluid circulation mechanism, since the replacement process requires a large amount of Mg-rich fluid interacting with the CaCO3 precursor. In the western end of the Neotethys, fault-controlled extensional basins developed during the Late Triassic spreading stage. In the Buda Hills and Danube-East blocks, distinct parts of silica and organic matter-rich slope and basinal deposits are dolomitized. Petrographic, geochemical, and fluid inclusion data distinguished two dolomite types: (1) finely to medium crystalline and (2) medium to coarsely crystalline. They commonly co-occur and show a gradual transition. Both exhibit breccia fabric under microscope. Dolomite texture reveals that the breccia fabric is not inherited from the precursor carbonates but was formed during the dolomitization process and under the influence of repeated seismic shocks. Dolomitization within the slope and basinal succession as well as within the breccia zones of the underlying basement block is interpreted as being related to fluid originated from the detachment zone and channelled along synsedimentary normal faults. The proposed conceptual model of dolomitization suggests that pervasive dolomitization occurred not only within and near the fault zones. Permeable beds have channelled the fluid towards the basin centre where the fluid was capable of partial dolomitization. The fluid inclusion data, compared with vitrinite reflectance and maturation data of organic matter, suggest that the ascending fluid was likely hydrothermal which cooled down via mixing with marine-derived pore fluid. Thermal gradient is considered as a potential driving force for fluid flow

Similarities and differences in the dolomitization history of two coeval Middle Triassic carbonate platforms, Balaton Highland, Hungary

Dolomitization of platform carbonates is commonly the result of multiphase processes. Documentation of the complex dolomitization history is difficult if completely dolomitized sections are studied. Two Middle Anisian sections representing two coeval carbonate platforms were investigated and compared in the present study. Both sections are made up of meter-scale peritidal–lagoonal cycles with significant pedogenic overprint. One of the sections contains non-dolomitized, partially dolomitized, and completely dolomitized intervals, whereas the other is completely dolomitized. Based on investigations of the partially dolomitized section, penecontemporaneous dolomite formation and/or very early post-depositional dolomitization were identified in various lithofacies types. In shallow subtidal facies, porphyrotopic dolomite was found preferentially in microbial micritic fabrics. Microbially induced dolomite precipitation and/or progressive replacement of carbonate sediments could be interpreted for stromatolites. Cryptocrystalline to very finely crystalline dolomite, probably of pedogenic origin, was encountered in paleosoil horizons. Fabric-destructive dolomite commonly found below these horizons was likely formed via reflux of evaporated seawater. As a result of the different paleogeographic settings of the two platforms, their shallow-burial conditions were significantly different. One of the studied sections was located at the basinward platform margin where pervasive fabric-retentive dolomitization took place in a shallow-burial setting, probably via thermal convection. In contrast, in the area of the other, smaller platform shallow-water carbonates were covered by basinal deposits, preventing fluid circulation and accordingly pervasive shallow-burial dolomitization. In the intermediate to deep burial zone, recrystallization of partially dolomitized limestone and occlusion of newly opened fractures and pores by coarsely crystalline dolomite took place