Abstract. For a given graph property Π (i.e., a collection Π of graphs), the Π-Contraction problem is to determine whether the input graph G can be transformed into a graph satisfying property Π by contracting at most k edges, where k is a parameter. In this paper, we mainly focus on the parameterized complexity of Π-Contraction problems for Π being H-free (i.e., containing no induced subgraph isomorphic to H) for various fixed graphs H.We show that Clique Contraction (equivalently, P3-Free Contraction for connected graphs) is FPT (fixed-parameter tractable) but admits no polynomial kernel unless NP ⊆ coN P/poly, and prove that Chordal Contraction (equivalently, {C l : l ≥ 4}-Free Contraction) is W[2]-hard. We completely characterize the parameterized complexity of H-Free Contraction for all fixed 3-connected graphs H: FPT but no polynomial kernel unless NP ⊆ coN P/poly if H is a complete graph, and W[2]-hard otherwise. We also show that H-Free Contraction is W[2]-hard whenever H is a fixed cycle C l for some l ≥ 4 or a fixed path P l for some odd l ≥ 5.
Human leukocyte antigen (HLA) class II plays critical roles in antigen presentation and the initiation of immune responses. However, the correlation between the HLA class II gene expression level and the survival of patients with breast cancer is still under investigation. We analyzed microarray and RNA-Seq data of breast cancer from the cancer genome atlas (TCGA), genotype-tissue expression (GTEx) and Oncomine databases by using bioinformatics tools. The expression of the HLA-DQA1, HLA-DQA2, and HLA-DQB2 genes was significantly upregulated in breast cancer. Higher expression levels of HLA class II genes in breast cancer, especially HLA-DOB and HLA-DQB2, were significantly associated with better overall survival. Furthermore, the expression of HLA class II genes was more closely associated with survival in breast cancer than in other cancer types. CD48 coexpressed with both HLA-DOB and HLA-DQB2 was also positively associated with the overall survival of breast cancer patients. The results indicated that HLA class II and CD48 may enhance antitumor immunity, and their expression patterns may serve as potential prognostic biomarkers and therapeutic targets in breast cancer.Abbreviations: CRC = colorectal cancer, DAVID = database for annotation, visualization and integrated discovery, GEPIA2 = gene expression profiling interactive analysis 2, GO = gene ontology, GTEx = genotype-tissue expression, HLA = human leukocyte antigen, HR = hazard ratio, OS = overall survival, STRING = search tool for the retrieval of interacting genes, TCGA = the cancer genome atlas.
We study the parameterized complexity of Split Contraction and Threshold Contraction. In these problems we are given a graph G and an integer k and asked whether G can be modified into a split graph or a threshold graph, respectively, by contracting at most k edges. We present an FPT algorithm for Split Contraction, and prove that Threshold Contraction on split graphs, i.e., contracting an input split graph to a threshold graph, is FPT when parameterized by the number of contractions. To give a complete picture, we show that these two problems admit no polynomial kernels unless N P ⊆ coN P/poly.
Eriocaulon buergerianum is a common Chinese medicinal herb and belongs to the family Eriocaulaceae genus Eriocaulon the annual herbs. In this study, the complete chloroplast genome of E. buergerianum was assembled and reported. The complete chloroplast genome of E. buergerianum is 157,016 bp in length as the circular, which harbours a large single-copy region (LSC) of 81,534 bp, a small single-copy region (SSC) of 17,114 bp, and two inverted-repeat regions (IRs) of 26,393 bp each one. The overall nucleotide content of the chloroplast genome: A of 31.8%, T of 32.4%, C of 18.2% G of 17.6%, and 35.8% GC content. The chloroplast genome of E. buergerianum contains 133 genes, which includes 88 protein-coding genes (PCGs), 37 transfer RNA (tRNAs), and 8 ribosome RNA (rRNAs). The evolutionary analysis used neighbour-joining (NJ) method and the result showed that E. buergerianum was closely related to Eriocaulon sexangulare in the family Eriocaulaceae. This study will be helpful for genome data and genomic resources of the family Eriocaulaceae for further.
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