Every planar graph without 4-cycles adjacent to two triangles is DP-4-colorable

Wang and Lih (2002) conjectured that every planar graph without adjacent triangles is 4-choosable. In this paper, we prove that every planar graph without any 4-cycle adjacent to two triangles is DP-4-colorable, which improves the results of Lam et al. (1999), Cheng et al. (2016) and Kim and Yu [ arXiv:1709.09809v1].     

Enantioselective Synthesis of Polycyclic Aromatic Hydrocarbon (PAH)-Based Planar Chiral Bent Cyclophanes by Rhodium-Catalyzed [2+2+2] Cycloaddition

The enantioselective synthesis of polycyclic aromatic hydrocarbon (PAH)-based planar chiral cyclophanes was achieved for the first time by the rhodium-catalyzed intramolecular regio- and enantioselective [2+2+2] cycloaddition of tethered diyne-benzofulvenes followed by stepwise oxidative transformations. The thus synthesized planar chiral bent cyclophanes, that possess bent p-terphenyl- and 9-fluorenone-cores, were converted to 9-fluorenol-based ones with excellent ee values of >99 % by diastereoselective 1,2-reduction. These 9-fluorenol-based cyclophanes exhibited high fluorescence quantum yields, which were significantly higher than that of an acyclic reference molecule (78–82 % vs. 48 %). The bending effect on the chiroptical property was also examined, which revealed that the anisotropy factors (g_abs values) for electronic circular dichroism (ECD) of these 9-fluorenol-based planar chiral bent cyclophanes increase as the tether length becomes shorter.     

Control of Axial Chirality by Planar Chirality Based on Optically Active [2.2]Paracyclophane

Optically active X-shaped molecules based on the planar chiral [2.2]paracyclophane building block were prepared, in which di(methoxy)terphenyl units were stacked on the central benzene rings. At 25 °C, anisolyl rings freely rotate in solution, while in the crystal form, they are fixed by intramolecular CH–π interactions, thereby leading to the expression of the axial chirality, i.e., propeller chirality was exhibited by the planar chiral [2.2]paracyclophane moiety. The X-shaped molecule exhibited good circularly polarized luminescence (CPL) profiles with moderate Φ_PL and a large g_lum value in the order of 10⁻³ at 25 °C, in solution. In contrast, at −120 °C, dual CPL emission with opposite signs was observed. According to the theoretical studies, the rotary motion of the anisolyl units is suppressed in the excited states, and so emission from two isomers could be observed. These results demonstrate that the axial chirality was controlled by the planar chirality, leading ultimately to propeller chirality.     

Nanosized Carbon Macrocycles Based on a Planar Chiral Pseudo Meta-[2.2]Paracyclophane

Structural designs combining cycloparaphenylenes (CPPs) backbone with planar chiral [2.2]paracyclophane ([2.2]PCP) lead to optical-active chiral macrocycles with intriguing properties. X-ray crystal analysis revealed aesthetic necklace-shaped structures and size-dependent packages with long-range channels. The macrocycles exhibit unique photophysical properties with high fluorescence quantum yield of up to 82 %, and the fluorescent color varies with ring size. In addition, size-dependent chiroptical properties with moderately large CPL dissymmetry factor of 10⁻³ and CPL brightness in the range of 30–40 M⁻¹ cm⁻¹ were observed.     

Using block designs in crossing number bounds

The crossing number $\mathrm{\text{CR}}\left(G\right)$ of a graph $G=\left(V,E\right)$ is the smallest number of edge crossings over all drawings of $G$ in the plane. For any $k\ge 1$, the $k$‐planar crossing number of $G,{\mathrm{\text{CR}}}_k\left(G\right)$, is defined as the minimum of $\text{CR}\left(G_1\right)+\text{CR}\left(G_2\right)+?+\text{CR}\left(G_k\right)$ over all graphs $G_1,G_2,\dots ,G_k$ with ${\cup }_{i=1}^k{G}_i=G$. Pach et al [Comput. Geom.: Theory Appl. 68 (2018), pp. 2–6] showed that for every $k\ge 1$, we have ${\text{CR}}_k\left(G\right)\le (2/k^2?1/k^3)\text{CR}\left(G\right)$ and that this bound does not remain true if we replace the constant $2/k^2?1/k^3$ by any number smaller than $1/k^2$. We improve the upper bound to $(1/k^2)\left(1+o\left(1\right)\right)$ as $k\to \infty$. For the class of bipartite graphs, we show that the best constant is exactly $1/k^2$ for every $k$. The results extend to the rectilinear variant of the $k$‐planar crossing number.     

固体核磁共振结合密度泛函理论计算研究SSZ-39分子筛的钠离子落位与铝分布

具有AEI结构的SSZ-39分子筛的骨架外阳离子落位和铝分布对其催化性能影响显著.AEI笼中有三个结晶学不等价位，且铝取代T位具有一定的倾向性.本文结合固体核磁共振（NMR）技术（²⁷Al/²³Na MQ MAS NMR），以及密度泛函理论（DFT）计算，研究了不同硅铝比Na-SSZ-39分子筛中的Na⁺落位和铝分布.在孤立铝分布的情况下，铝原子优先占据于T3位，Na⁺主要落位于AEI笼中的SIIa0和SIII'a0位点上，其中SIII'a0位点的优先度较高，此外少部分Na⁺还落位于六棱柱内部的SIa0.当铝对存在时，AlSiSiAl分布的铝对占据六元环的对位（T3-T3），对应的Na⁺分别落位于SIIa1和SⅢ'a1位点.随着分子筛结构的部分破坏，游离的Na⁺可能形成明显的SIII'b位点.本文可加深对SSZ-39分子筛构效关系的理解，为更好地调控催化性能奠定基础.     

中国出境旅游的外交效应

2000年以来，中国出境旅游高增长、高消费，影响力不断增大，成为国家外交战略的重要内容，外交效应逐渐显现。通过辨析中国出境旅游外交效应的概念、表现形式和结果，基于10个中国主要出境目的国的旅游互动数据，采用DIF-GMM计量经济模型，实证检验了中国出境旅游外交效应。结果表明，中国通过有序推进ADS协议、加强经济援助、举办“旅游年”活动、实施旅游“制裁”，并积极参与国际制度建设等旅游外交行为，促进了与世界各国的友好交往，维护了自身核心利益，提升了外交软实力和国际影响力。国际旅游反作用于国际关系，对国际关系具有显著的正向促进作用，不仅是国际关系的结果，而且是其重要动因之一。中国出境旅游与政治、经济、社会、文化等联动，多方面提升了中国的国际影响力。     

A survey on book-embedding of planar graphs

The book-embedding problem arises in several area, such as very large scale integration (VLSI) design and routing multilayer printed circuit boards (PCBs). It can be used into various practical application fields. A book embedding of a graph G is an embedding of its vertices along the spine of a book, and an embedding of its edges to the pages such that edges embedded on the same page do not intersect. The minimum number of pages in which a graph G can be embedded is called the pagenumber or book-thickness of the graph G. It is an important measure of the quality for book-embedding. It is NP-hard to research the pagenumber of book-embedding for a graph G. This paper summarizes the studies on the book-embedding of planar graphs in recent years.     

Structural study of a manganese(II) `picket‐fence' porphyrin complex

`Picket‐fence' porphyrin compounds are used in the investigation of interactions of hemes with dioxygen, carbon monoxide, nitric monoxide and imidazole ligands. (Cryptand‐222)potassium chlorido[meso‐tetra(α,α,α,α‐o‐pivalamidophenyl)porphyrinato]manganese tetrahydrofuran monosolvate (cryptand‐222 is 4,7,13,16,21,24‐hexaoxa‐1,10‐diazabicyclo[8.8.8]hexacosane), [K(C₁₈H₃₆N₂O₆)][Mn(C₆₄H₆₄N₈O₄)Cl]·C₄H₈O or [K(222)][Mn(TpivPP)Cl]·THF [systematic name for TpivPP: 5,10,15,20‐tetrakis(2‐tert‐butanamidophenyl)porphyrin], is a five‐coordinate high‐spin manganese(II) picket‐fence porphyrin complex. It crystallizes with a potassium cation chelated inside a cryptand‐222 molecule; the average K—O and K—N distances are 2.83 (4) and 2.995 (13) Å, respectively. All four protecting tert‐butyl pickets of the porphyrin are ordered. The porphyrin plane is nearly planar, as indicated by the atomic displacements and the dihedral angles between the mean planes of the pyrrole rings and the 24‐atom mean plane. The axial chloride ligand is located inside the molecular cavity on the hindered porphyrin side and the Mn—Cl bond is tilted slightly off the normal to the porphyrin plane by 3.68 (2)°. The out‐of‐plane displacement of the metal centre relative to the 24‐atom mean plane (Δ₂₄) is 0.7013 (4) Å, indicating a noticeable porphyrin core doming.