A 2-distance coloring of a graph is a coloring of the vertices such that two vertices at distance at most two receive distinct colors.A list assignment of a graph G is a mapping L which assigns to each vertex v a set ...A 2-distance coloring of a graph is a coloring of the vertices such that two vertices at distance at most two receive distinct colors.A list assignment of a graph G is a mapping L which assigns to each vertex v a set L(v)of positive integers.The list 2-distance chromatic number of G denoted byχ_(2)^(l)(G)is the least integer k for which G is list 2-distance k-colorable.In this paper,we prove that every planar graph with g(G)≥5 and△(G)≥40 is list 2-distance(△(G)+4)-colorable.展开更多
A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are con...A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.展开更多
Although a few cases of genetic epistasis in plants have been reported, the combined analysis of genetically phenotypic segregation and the related molecular mechanism remains rarely studied. Here, we have identified ...Although a few cases of genetic epistasis in plants have been reported, the combined analysis of genetically phenotypic segregation and the related molecular mechanism remains rarely studied. Here, we have identified a gene(named GaPC) controlling petal coloration in Gossypium arboreum and following a heritable recessive epistatic genetic model. Petal coloration is controlled by a single dominant gene,GaPC. A loss-of-function mutation of GaPC leads to a recessive gene Gapc that masks the phenotype of other color genes and shows recessive epistatic interactions. Map-based cloning showed that GaPC encodes an R2R3-MYB transcription factor. A 4814-bp long terminal repeat retrotransposon insertion at the second exon led to GaPC loss of function and disabled petal coloration. GaPC controlled petal coloration by regulating the anthocyanin and flavone biosynthesis pathways. Expression of core genes in the phenylpropanoid and anthocyanin pathways was higher in colored than in white petals. Petal color was conferred by flavonoids and anthocyanins, with red and yellow petals rich in anthocyanin and flavonol glycosides, respectively. This study provides new insight on molecular mechanism of recessive epistasis,also has potential breeding value by engineering GaPC to develop colored petals or fibers for multifunctional utilization of cotton.展开更多
Bollobas and Gyarfas conjectured that for n 〉 4（k - 1） every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k ＋ 2 vertices. Liu, et al. proved that the conjecture holds when...Bollobas and Gyarfas conjectured that for n 〉 4（k - 1） every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k ＋ 2 vertices. Liu, et al. proved that the conjecture holds when n 〉 13k - 15. In this note, we characterize all the 2-edge-colorings of Kn where each monochromatic k-connected subgraph has at most n - 2k ＋ 2 vertices for n ≥ 13k - 15.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11771443,12071265)。
文摘A 2-distance coloring of a graph is a coloring of the vertices such that two vertices at distance at most two receive distinct colors.A list assignment of a graph G is a mapping L which assigns to each vertex v a set L(v)of positive integers.The list 2-distance chromatic number of G denoted byχ_(2)^(l)(G)is the least integer k for which G is list 2-distance k-colorable.In this paper,we prove that every planar graph with g(G)≥5 and△(G)≥40 is list 2-distance(△(G)+4)-colorable.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62105004 and 52174141)the College Student Innovation and Entrepreneurship Fund Project(Grant No.202210361053)+1 种基金Anhui Mining Machinery and Electrical Equipment Coordination Innovation Center,Anhui University of Science&Technology(Grant No.KSJD202304)the Anhui Province Digital Agricultural Engineering Technology Research Center Open Project(Grant No.AHSZNYGC-ZXKF021)。
文摘A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.
基金supported by the Fundamental Research Funds for the Central Universities(KYZZ2022003)Jiangsu Collaborative Innovation Center for Modern Crop Production project (No.10)。
文摘Although a few cases of genetic epistasis in plants have been reported, the combined analysis of genetically phenotypic segregation and the related molecular mechanism remains rarely studied. Here, we have identified a gene(named GaPC) controlling petal coloration in Gossypium arboreum and following a heritable recessive epistatic genetic model. Petal coloration is controlled by a single dominant gene,GaPC. A loss-of-function mutation of GaPC leads to a recessive gene Gapc that masks the phenotype of other color genes and shows recessive epistatic interactions. Map-based cloning showed that GaPC encodes an R2R3-MYB transcription factor. A 4814-bp long terminal repeat retrotransposon insertion at the second exon led to GaPC loss of function and disabled petal coloration. GaPC controlled petal coloration by regulating the anthocyanin and flavone biosynthesis pathways. Expression of core genes in the phenylpropanoid and anthocyanin pathways was higher in colored than in white petals. Petal color was conferred by flavonoids and anthocyanins, with red and yellow petals rich in anthocyanin and flavonol glycosides, respectively. This study provides new insight on molecular mechanism of recessive epistasis,also has potential breeding value by engineering GaPC to develop colored petals or fibers for multifunctional utilization of cotton.
基金Supported by the National Natural Science Foundation of China(10701065 and 11101378)Zhejiang Provincial Natural Science Foundation(LY14A010009)
文摘Bollobas and Gyarfas conjectured that for n 〉 4（k - 1） every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k ＋ 2 vertices. Liu, et al. proved that the conjecture holds when n 〉 13k - 15. In this note, we characterize all the 2-edge-colorings of Kn where each monochromatic k-connected subgraph has at most n - 2k ＋ 2 vertices for n ≥ 13k - 15.
