Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characteri...Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.展开更多
Considering the advantages of single nucleotide polymorphisms（SNP） in genotyping and variety identification, the first set public SNP markers at Cotton Marker Database（http：//www.cottonmarker.org/） were validated...Considering the advantages of single nucleotide polymorphisms（SNP） in genotyping and variety identification, the first set public SNP markers at Cotton Marker Database（http：//www.cottonmarker.org/） were validated and screened across standard varieties of cotton distinctness, uniformity and stability（DUS） test, aiming to obtain an appropriate set of core SNP markers suitable for upland cotton cultivars in China. A total of 399 out of 1 005 SNPs from 270 loci including 170 insertions-deletions（In Dels） were evaluated for their polymorphisms among 30 standard varieties using Sanger sequencing. As a result, 147 loci were sequenced successfully, 377 SNPs and 49 In Dels markers were obtained. Among the 377 SNP markers, 333 markers（88.3%） were polymorphic between Gossypium hirsutum and G. barbadense, while 164 markers（43.5%） were polymorphic within upland cotton. As for In Del markers, the polymorphic rate is relatively lower than that of SNP both between species and within species. The homozygous DNA locus ratio of 121 SNPs was higher than 86.2% while that of other 43 SNPs was less than 70%. Only 64 SNPs displayed completely homozygous genotypes among all of the detected upland cotton varieties with 100% homozygous DNA locus ratio. At last, a set of 23 pairs of core SNPs were achieved in view of avoidance of linkage, with polymorphism information content（PIC） values varying from 0.21 to 0.38 with an average of 0.28. Genotype characteristics and genetic diversity were analyzed based on the set of core markers, while 40 pairs of core simple-sequence repeats（SSR） primers comprised of 10 sets of four multiplex PCR combinations were also used for analysis based on fluorescence detection system. Comparison results indicated that the genetic diversity level was almost equal, while various varieties were significantly different from each other. Genetic relationship revealed by SSR markers is related to geographic source to a certain extent. Meanwhile clustering results analyzed by SNP markers are more consistent with kinship, which demonstrated that the screen strategy for core SNP marker is effective.展开更多
基金Supported by the Natural Science Foundation of China(12131013,12371356)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002015)the Fundamental Research Program of Shanxi Province(202303021221064).
文摘Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.
基金supported by the the Basic R&D Operation Special Fund for the Central Level, Non-Profit, Scientific Research Institutes, Ministry of Agriculture, China (1610162015A08)the National Key Technologies R&D Program of China during the 12th Five-Year Plan period (2011BAD35B09)
文摘Considering the advantages of single nucleotide polymorphisms（SNP） in genotyping and variety identification, the first set public SNP markers at Cotton Marker Database（http：//www.cottonmarker.org/） were validated and screened across standard varieties of cotton distinctness, uniformity and stability（DUS） test, aiming to obtain an appropriate set of core SNP markers suitable for upland cotton cultivars in China. A total of 399 out of 1 005 SNPs from 270 loci including 170 insertions-deletions（In Dels） were evaluated for their polymorphisms among 30 standard varieties using Sanger sequencing. As a result, 147 loci were sequenced successfully, 377 SNPs and 49 In Dels markers were obtained. Among the 377 SNP markers, 333 markers（88.3%） were polymorphic between Gossypium hirsutum and G. barbadense, while 164 markers（43.5%） were polymorphic within upland cotton. As for In Del markers, the polymorphic rate is relatively lower than that of SNP both between species and within species. The homozygous DNA locus ratio of 121 SNPs was higher than 86.2% while that of other 43 SNPs was less than 70%. Only 64 SNPs displayed completely homozygous genotypes among all of the detected upland cotton varieties with 100% homozygous DNA locus ratio. At last, a set of 23 pairs of core SNPs were achieved in view of avoidance of linkage, with polymorphism information content（PIC） values varying from 0.21 to 0.38 with an average of 0.28. Genotype characteristics and genetic diversity were analyzed based on the set of core markers, while 40 pairs of core simple-sequence repeats（SSR） primers comprised of 10 sets of four multiplex PCR combinations were also used for analysis based on fluorescence detection system. Comparison results indicated that the genetic diversity level was almost equal, while various varieties were significantly different from each other. Genetic relationship revealed by SSR markers is related to geographic source to a certain extent. Meanwhile clustering results analyzed by SNP markers are more consistent with kinship, which demonstrated that the screen strategy for core SNP marker is effective.
