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Decomposing Berge graphs [PDF]
A hole in a graph is an induced cycle on at least four vertices. A graph is Berge if it has no old hole and if its complement has no odd hole. In 2002, Chudnovsky, Robertson, Seymour and Thomas proved a decomposition theorem for Berge graphs saying that ...
Nicolas Trotignon
core
Advanced Materials, EarlyView.The energetic offset between the donor and the acceptor components in organic photoactive layers is central to the tradeoff between photovoltage and photocurrent losses. This Perspective covers the most important issues surrounding this topic in non‐fullerene acceptor blends, from the difficulty of accurately determining state energies and driving ...
Dieter Neher, Manasi Pranav
wiley +1 more source
Advanced Materials, EarlyView.We introduce a computational workflow that combines quantum chemical calculations and machine learning techniques to predict the catalytic performance of a wide range of catalysts in the nitrogen reduction reaction (NRR). The analysis of the trained models provides insights into the complex structure–activity relationship in experimental catalytic ...
Leonardo Di Ciano +5 more
wiley +1 more source
Journal of MathematicsA perfect Roman 3-dominating function on a graph G=V,E is a function f:V⟶0,1,2,3 having the property that if fv=0, then ∑u∈Nvfu=3, and if fv=1, then ∑u∈Nvfu=2 for any vertex v∈V.
Ahlam Almulhim
doaj +1 more source
Decomposing Berge graphs and detecting balanced skew partitions [PDF]
We prove that the problem of deciding whether a graph has a balanced skew partition is NP-hard. We give an O(n9)-time algorithm for the same problem restricted to Berge graphs.
Nicolas Trotignon
core
Layered Nanoporous Platforms for SERS Sensing
Advanced Materials Interfaces, EarlyView.Here, we present a detailed investigation of the SERS performance of layered nanoporous metals. The controlled deposition of well‐defined, stacked porous layers enabled a systematic analysis of the effects of multimetallic systems in SERS experiments. Numerical models are also used to support the experimental findings.
Yanqiu Zou +18 more
wiley +1 more source
On the perfect graph conjecture
Discrete Mathematics, 1976 We prove the following theorem: If every, odd cycle of length ≥5 has at least two chords, then the graph is perfect. This generalizes a result of Gallai and Suranyi and also a result of Olaru and Sachs.
openaire +1 more source
A new decomposition theorem for Berge graphs [PDF]
A hole in a graph is an induced cycle on at least four vertices. A graph is Berge if it has no odd hole and if its complement has no odd hole. In 2002, Chudnovsky, Robertson, Seymour and Thomas proved a decomposition theorem for Berge graphs saying that ...
Nicolas Trotignon
core
Advanced Materials Technologies, EarlyView.Left: Illustration of the glass & nanostructures system and the NIR emission at 1.5 µm, where the colored spheres represent the Er3+ ions within the doped glass. Right: Representation of the Stark splitting of the 4I13/2 and 4I15/2 manifolds of the Er3+, illustrating how the plasmonic modes facilitate the emission from the broader Stark manifold ...
Gaston Lozano Calderón +5 more
wiley +1 more source
Grounding Large Language Models for Robot Task Planning Using Closed‐Loop State Feedback
Advanced Robotics Research, EarlyView.BrainBody‐Large Language Model (LLM) introduces a hierarchical, feedback‐driven planning framework where two LLMs coordinate high‐level reasoning and low‐level control for robotic tasks. By grounding decisions in real‐time state feedback, it reduces hallucinations and improves task reliability.
Vineet Bhat +4 more
wiley +1 more source