This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be i...This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.展开更多
Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G ...Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.展开更多
Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connec...Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connectivity for a bipartite (mg,mf)-graph to have a (g,f)-factor with special properties are obtained and some previous results are generalized.Furthermore,the new results are proved to be the best possible.展开更多
In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of ...In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.展开更多
BACKGROUND A series of long non-coding RNAs(lncRNAs)have been reported to play a crucial role in cancer biology.Some previous studies report that lncRNA CDKN2B-AS1 is involved in some human malignancies.However,its ro...BACKGROUND A series of long non-coding RNAs(lncRNAs)have been reported to play a crucial role in cancer biology.Some previous studies report that lncRNA CDKN2B-AS1 is involved in some human malignancies.However,its role in hepatocellular carcinoma(HCC)has not been fully deciphered.AIM To decipher the role of CDKN2B-AS1 in the progression of HCC.METHODS CDKN2B-AS1 expression in HCC was detected by quantitative real-time polymerase chain reaction.The malignant phenotypes of Li-7 and SNU-182 cells were detected by the CCK-8 method,EdU method,and flow cytometry,respectively.RNA immunoprecipitation was executed to confirm the interaction between CDKN2B-AS1 and E2F transcription factor 1(E2F1).Luciferase reporter assay and chromatin immunoprecipitation were performed to verify the binding of E2F1 to the promoter of G protein subunit alpha Z(GNAZ).E2F1 and GNAZ were detected by western blot in HCC cells.RESULTS In HCC tissues,CDKN2B-AS1 was upregulated.Depletion of CDKN2B-AS1 inhibited the proliferation of HCC cells,and the depletion of CDKN2B-AS1 also induced cell cycle arrest and apoptosis.CDKN2B-AS1 could interact with E2F1.Depletion of CDKN2B-AS1 inhibited the binding of E2F1 to the GNAZ promoter region.Overexpression of E2F1 reversed the biological effects of depletion of CDKN2B-AS1 on the malignant behaviors of HCC cells.CONCLUSION CDKN2B-AS1 recruits E2F1 to facilitate GNAZ transcription to promote HCC progression.展开更多
基金This work is supported by NNSF of ChinaRFDP of Higher Education
文摘This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.
基金This work was supported by NNSF. RFDP and NNSF of shandong province(Z2000A02 ).
文摘Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.
基金Supported by the National Natural Science Foundation of China( 60 1 72 0 0 3) NSF of Shandongprovince ( Z2 0 0 0 A0 2 )
文摘Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connectivity for a bipartite (mg,mf)-graph to have a (g,f)-factor with special properties are obtained and some previous results are generalized.Furthermore,the new results are proved to be the best possible.
基金This work is supported by NSFC (10471078.10201019)RSDP (20040422004) of China
文摘In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.
文摘BACKGROUND A series of long non-coding RNAs(lncRNAs)have been reported to play a crucial role in cancer biology.Some previous studies report that lncRNA CDKN2B-AS1 is involved in some human malignancies.However,its role in hepatocellular carcinoma(HCC)has not been fully deciphered.AIM To decipher the role of CDKN2B-AS1 in the progression of HCC.METHODS CDKN2B-AS1 expression in HCC was detected by quantitative real-time polymerase chain reaction.The malignant phenotypes of Li-7 and SNU-182 cells were detected by the CCK-8 method,EdU method,and flow cytometry,respectively.RNA immunoprecipitation was executed to confirm the interaction between CDKN2B-AS1 and E2F transcription factor 1(E2F1).Luciferase reporter assay and chromatin immunoprecipitation were performed to verify the binding of E2F1 to the promoter of G protein subunit alpha Z(GNAZ).E2F1 and GNAZ were detected by western blot in HCC cells.RESULTS In HCC tissues,CDKN2B-AS1 was upregulated.Depletion of CDKN2B-AS1 inhibited the proliferation of HCC cells,and the depletion of CDKN2B-AS1 also induced cell cycle arrest and apoptosis.CDKN2B-AS1 could interact with E2F1.Depletion of CDKN2B-AS1 inhibited the binding of E2F1 to the GNAZ promoter region.Overexpression of E2F1 reversed the biological effects of depletion of CDKN2B-AS1 on the malignant behaviors of HCC cells.CONCLUSION CDKN2B-AS1 recruits E2F1 to facilitate GNAZ transcription to promote HCC progression.
