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Perfect divisibility and perfect-Pollyanna in bull-free graphs
arXiv:2603.21538v2 Announce Type: replace-cross Abstract: A graph $G$ is {\em perfectly divisible} if, for each induced subgraph $H$ of $G$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $\omega(H[B])<\omega(H)$. A {\em bull} is a graph consisting of a triangle with two disjoint pendant edges. Ho\`ang [Discrete Math. 349 (2026) 114809] proposed four conjectures: 1.
Chirality Transfer to the Magnetic Sublattice in the Hybrid Perovskite (R)-/(S)-3-Fluoropyrrolidinium Copper(II) Chloride
arXiv:2604.22952v2 Announce Type: replace-cross Abstract: Incorporating chiral organic cations into organic-inorganic hybrid materials has been shown to enable the inorganic sublattice to display chiroptical properties. We report a new two-dimensional magnetic ($S=1/2$) chiral metal halide material, (R)- and (S)-$(C_4H_9FN)_2CuCl_4$ (where $(C_4H_9FN)^+$ is 3-fluoropyrrolidinium), which consists of Cu-Cl inorganic layers separated by $(C_4H_9FN)^+$ organic cations.
1 in 4 births in England now by emergency C-section
A quarter of all babies in England are now delivered by emergency caesarean operations, BBC analysis shows - marking a significant rise over the last five years.
1 in 4 births in England now by emergency C-section
A quarter of all babies in England are now delivered by emergency caesarean operations, BBC analysis shows - marking a significant rise over the last five years.