A full-homomorphism from a graph $G$ to a graph $H$ is a function on vertex sets that preserves adjacency and non-adjacency of vertices. A graph $G$ is called a minimal $H$-obstruction if it has no full-homomorphism to $H$ but every proper vertex induced subgraph of $G$ does. Such graphs can have at most $|V(H)|+1$ vertices. The set of minimal $H$-obstructions on $|V(H)|+1$ vertices is denoted by $\mathrm{obs*}(H)$. In question 2 of the paper"Santiago Guzm{\'a}n-Pro, Full-homomorphisms to paths and cycles, Discrete Mathematics, 347(3):113800, 2024"it is asked if there is a characterization of those graphs $G$ that lie in $\mathrm{obs*}(H)$ for some graph $H$. In this paper, we give a complete answer to this question.
Zahra Rahimi, M. H. Shirdareh Haghighi, Asma Namazi Department of Mathematics et al.· 0 citations
The discovery of high-temperature ferromagnetism in the metallic van der Waals (vdW) system Fe$_N$GeTe$_2$ has brought two-dimensional (2D) magnets into technologically relevant temperature scales. Specifically at N = 5, dilution of magnetic moments by nickel substitution counterintuitively achieves a record high Curie temperature of 478~K. Unraveling the origin of this nickel-substitution-induced enhancement is complicated by the compound's structural complexity, coexistent itinerant and local magnetic contributions, and mesoscopic compositional domains. Through coordinated structural and electronic characterization, we identify that the high-T$_C$ magnetic phase arises from a strain-stabilized Fe$_6$GeTe$_2$ nano-precipitate. Combining first-principles calculations and spin- and angle-resolved photoemission spectroscopy (ARPES), we uncover a site-specific electronic landscape in which interior iron atoms primarily host localized moments while the outer iron atoms neighboring the tellurium layers produce spin-polarized itinerant carriers that cross the vdW gap. The large energy cost associated with homogeneous nickel substitution is found to favor the spontaneous precipitation of the crystallographically and electronically ``clean''high-T$_C$ phase. Finally, we compare metal-rich vdW magnets with binary magnetic alloys, and discuss the unifying roles of nano-precipitates in stabilizing otherwise unattainable bulk phases. Our work provides mechanistic insights into the record-high T$_C$ ferromagnetism in (Fe,Ni)$_{5+\delta}$GeTe$_2$, establishing a rigorous foundation for the atomic engineering of vdW magnetic metals informed by direct electronic signatures.
T. Werner, Jonathan T. Reichanadter, Xiang Chen et al.· 0 citations
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