The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum deg...The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum degree Δ≥9, then χ'' (G) = Δ + 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without intersecting chordal 4-cycles, then χ ''(G) = 9.展开更多
In this paper we consider the problem of finding the smallest number such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most elements. We solve this proble...In this paper we consider the problem of finding the smallest number such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most elements. We solve this problem for n sufficiently large.展开更多
A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color.In this paper,it is proved that if G is a planar graph with...A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color.In this paper,it is proved that if G is a planar graph with Δ（G） ≥ 7 and without chordal 7-cycles,then G has a（Δ（G） ＋ 1）-total-coloring.展开更多
CH_(4) emission rates followed an increased pattern during the growing season at Tibetan Plateau.•Unique genes carried by abundant species were positively correlated with CH_(4) emission rates.•Climate factors influen...CH_(4) emission rates followed an increased pattern during the growing season at Tibetan Plateau.•Unique genes carried by abundant species were positively correlated with CH_(4) emission rates.•Climate factors influenced CH_(4) emission rates by regulating microbial community and their genes.Microorganisms play pivotal roles in soil methane(CH_(4))emissions and their functional genes are origins of a key mechanism for soil CH4-cycling.However,understanding of the roles of specific genes(e.g.,unique or shared genes carried by species)underlying CH_(4)-cycling remains elusive.Here,we measured CH_(4) emission rates and investigated variations in microbial community and the abundance of genes carried by species during the growing season in alpine meadow on the Tibetan Plateau.We discovered that CH_(4) emission rates increased from 394.4,745.9,and 1092.7µg CH4 m−2 h−1,in April,June,and August,respectively,and had a positive correlation with unique genes carried by abundant species during the growing season.Moreover,we found that unique genes carried by abundant species involved in methanogenesis processes have a higher abundance than methanotrophic processes.Further analysis indicated that climate factors(i.e.,mean monthly temperature(MMT)and mean monthly precipitation(MMP))influenced microbial community and their functional genes,and therefore affected the CH_(4) emission rates.Overall,the present study provides a novel insight into the variation of soil CH4 emissions from a functional gene perspective,highlighting the important roles of unique genes carried by abundant species in CH4 emissions in the Tibetan Plateau under seasonal variation.展开更多
基金supported by Natural Science Foundation of Shandong Province (Grant No. ZR2009AM009)Scientific Research Foundation for the Excellent Middle-Aged and Youth Scientists of Shandong Province (Grant No. BS2012SF016)National Natural Science Foundation of China (Grant Nos.11001055 and 11101243)
文摘The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum degree Δ≥9, then χ'' (G) = Δ + 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without intersecting chordal 4-cycles, then χ ''(G) = 9.
基金support from FCT—Fundacao para a Ciencia e a Tecnologia(Portugal),through Projects PTDC/MAT/113207/2009PEst-OE/MAT/UI0297/2011(CMA).
文摘In this paper we consider the problem of finding the smallest number such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most elements. We solve this problem for n sufficiently large.
基金Supported by National Natural Science Foundation of China(Grant No.11271006)
文摘A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color.In this paper,it is proved that if G is a planar graph with Δ（G） ≥ 7 and without chordal 7-cycles,then G has a（Δ（G） ＋ 1）-total-coloring.
基金financially supported by the National Natural Science Foundation of China(Grant No.42277284)the 2021 first funds for central government to guide local science and technology development in Qinghai Province(Grant No.2021ZY002)the Second Tibetan Plateau Scientific Expedition and Research Program(Grant Nos.2019QZKK020102,2019OZKK0302).
文摘CH_(4) emission rates followed an increased pattern during the growing season at Tibetan Plateau.•Unique genes carried by abundant species were positively correlated with CH_(4) emission rates.•Climate factors influenced CH_(4) emission rates by regulating microbial community and their genes.Microorganisms play pivotal roles in soil methane(CH_(4))emissions and their functional genes are origins of a key mechanism for soil CH4-cycling.However,understanding of the roles of specific genes(e.g.,unique or shared genes carried by species)underlying CH_(4)-cycling remains elusive.Here,we measured CH_(4) emission rates and investigated variations in microbial community and the abundance of genes carried by species during the growing season in alpine meadow on the Tibetan Plateau.We discovered that CH_(4) emission rates increased from 394.4,745.9,and 1092.7µg CH4 m−2 h−1,in April,June,and August,respectively,and had a positive correlation with unique genes carried by abundant species during the growing season.Moreover,we found that unique genes carried by abundant species involved in methanogenesis processes have a higher abundance than methanotrophic processes.Further analysis indicated that climate factors(i.e.,mean monthly temperature(MMT)and mean monthly precipitation(MMP))influenced microbial community and their functional genes,and therefore affected the CH_(4) emission rates.Overall,the present study provides a novel insight into the variation of soil CH4 emissions from a functional gene perspective,highlighting the important roles of unique genes carried by abundant species in CH4 emissions in the Tibetan Plateau under seasonal variation.
