Packing TT-connectors in graphs needs more connectivity

Strengthening the classical concept of Steiner trees, West and Wu [J. Combin. Theory Ser. B 102 (2012), 186--205] introduced the notion of a $T$-connector in a graph $G$ with a set $T$ of terminals. They conjectured that if the set $T$ is $3k$-edge-connected in $G$, then $G$ contains $k$ edge-disjoint $T$-connectors. We disprove this conjecture by constructing infinitely many counterexamples for $k=1$ and for each even $k$

A necessary and sufficient condition for the existence of a properly coloured ff-factor in an edge-coloured graph

The main result of this paper is an edge-coloured version of Tutte's $f$-factor theorem. We give a necessary and sufficient condition for an edge-coloured graph $G^c$ to have a properly coloured $f$-factor. We state and prove our result in terms of an auxiliary graph $G_f^c$ which has a 1-factor if and only if $G^c$ has a properly coloured $f$-factor; this is analogous to the "short proof" of the $f$-factor theorem given by Tutte in 1954. An alternative statement, analogous to the original $f$-factor theorem, is also given. We show that our theorem generalises the $f$-factor theorem; that is, the former implies the latter. We consider other properties of edge-coloured graphs, and show that similar results are unlikely for $f$-factors with rainbow components and distance-$d$-coloured $f$-factors, even when $d=2$ and the number of colours used is asymptotically minimal.Comment: 18 pages, 5 figure

The 2018 European heatwave led to stem dehydration but not to consistent growth reductions in forests

Publisher Copyright: © 2022, The Author(s).Heatwaves exert disproportionately strong and sometimes irreversible impacts on forest ecosystems. These impacts remain poorly understood at the tree and species level and across large spatial scales. Here, we investigate the effects of the record-breaking 2018 European heatwave on tree growth and tree water status using a collection of high-temporal resolution dendrometer data from 21 species across 53 sites. Relative to the two preceding years, annual stem growth was not consistently reduced by the 2018 heatwave but stems experienced twice the temporary shrinkage due to depletion of water reserves. Conifer species were less capable of rehydrating overnight than broadleaves across gradients of soil and atmospheric drought, suggesting less resilience toward transient stress. In particular, Norway spruce and Scots pine experienced extensive stem dehydration. Our high-resolution dendrometer network was suitable to disentangle the effects of a severe heatwave on tree growth and desiccation at large-spatial scales in situ, and provided insights on which species may be more vulnerable to climate extremes.Peer reviewe

Model-Based Design of Smart Home Control

This work deals with model-based design of Smart Home control and implementation of this system. The goal is to create a model that serves as a design and according to this model implement the system. Model-based programming tools do this well. The work first describes the model-based design, the modeling languages that are used to create such a design and the technologies that are used in Smart Home. Based on this knowledge, the model is created as a design using the SysML modeling language and then this design is implemented using PowerDEVS and Node-RED

Model-Based Design of Smart Home Control

Tato práce se zabývá návrhem, který je založený na modelu, řídicího systému Smart Home a následnou realizací tohoto systému. Cílem je vytvořit model, který slouží jako návrh, a podle tohoto modelu i realizovat systém. K tomu dobře slouží programovací nástroje, které fungují na bázi modelu. V práci je nejprve popsán na modelech založený návrh, modelovací jazyky, které slouží k tvorbě takového návrhu, a technologie, které se ve Smart Home používají. Na základě těchto poznatků je vytvořen model jako návrh pomocí modelovacího jazyku SysML a následně je tento návrh realizován pomocí programů PowerDEVS a Node-RED.This work deals with model-based design of Smart Home control and implementation of this system. The goal is to create a model that serves as a design and according to this model implement the system. Model-based programming tools do this well. The work first describes the model-based design, the modeling languages that are used to create such a design and the technologies that are used in Smart Home. Based on this knowledge, the model is created as a design using the SysML modeling language and then this design is implemented using PowerDEVS and Node-RED.

Úplný bipartitní graf bez dobře obarvených kružnic délky 4

V článku je získán globální výsledek o dekompozici hranově obarvených úplných bipartitních grafů bez dobře obarvených kružnic délky 4. Jako důsledek je získán výsledek o existenci monochromatické hvězdy.The paper gives a global decomposition theorem for edge‐colorings of complete bipartite graphs without properly colored C4. As a corollary, a result on the existence of a monochromatic star is obtained

Dvojice zakázaných podgrafů a 2-souvislé supereulerovské grafy

Je dokázáno, že 2-souvislý graf bez K_{1,3} obsauje eulerovský faktor, pokud je graf bez indukovaného N_{1,1,4} nebo N_{1,2,2} nebo Z_5 nebo P_8. Příslušné výsledky pro hamiltonicitu jsou rovněž odvozeny.It is proved that a 2-connected claw-free graph admits a spanning Eulerian subgraph if it is N_{1,1,4} or N_{1,2,2} or Z_5 or P_8-free. Related hamiltonicity results are also obtained