Turán number of Berge linear forests in uniform hypergraphs

Let F be a graph and H be a hypergraph.We say that H contains a Berge-F If there exists a bijectionψ:E(F)→E(H)such that for Ve E E(F),e C(e),and the Turan number of Berge-F is defined to be the maximum number of edges in an r-uniform hypergraph of order n that is Berge-F-free,denoted by ex,(n,Berge-F).A linear forest is a graph whose connected components are all paths or isolated vertices.Let Ln,k be the family of all linear forests of n vertices with k edges.In this paper,Turan number of Berge-Ln,in an r-uniform hypergraph is studied.When r≥k+1 and 3≤r≤l[]=1,we determine 2 the exact value of ex,(n,Berge-Ln,)respectively.When K-1≤r≤k,we 2 determine the upper bound of ex,(n,Berge-Ln,).

On the Turán Numbers of Linear Forests in Bipartite Graphs

A linear forest is a graph consisting of paths.In this paper,the authors determine the maximum number of edges in an(m,n)-bipartite graph which does not contain a linear forest consisting of paths on at least four vertices for n≥m when m is sufficiently large.

PARTITIONING CIRCULANT GRAPHS INTOISOMORPHIC LINEAR FORESTS

It is a well known fact that the linear arboricity of a k-regular graph is [(k+1)/2] fork=3,4. In this paper, we prove that if the number Of edges of a k-regular circulant is divisibleby [(k+1)/2], then its edge set can be partitioned into [(k+1)/2] isomorphic linear forests, fork=3,4.

Strong Labelings of Linear Forests

A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}. In this paper, we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees （mT）, all of them of the same order, grows at least exponentially with m.

Linear arboricity of Cartesian products of graphs

A linear forest is a forest whose components are paths. The linear arboricity la （G） of a graph G is the minimum number of linear forests which partition the edge set E（G） of G. The Cartesian product G□H of two graphs G and H is defined as the graph with vertex set V（G□H） = {（u, v）｜ u ∈V（G）, v∈V（H） } and edge set E（G□H） = { （ u, x） （ v, Y）｜u=v and xy∈E（H）, or uv∈E（G） and x=y}. Let Pm and Cm,, respectively, denote the path and cycle on m vertices and K, denote the complete graph on n vertices. It is proved that （Km□Pm）=[n＋1/2]for m≥2,la（Km□Cm）=[n＋2/2],and la（Km□Km）=[n＋m-1/2]. The methods to decompose these graphs into linear forests are given in the proofs. Furthermore, the linear arboricity conjecture is true for these classes of graphs.

Mapping Soil Organic Carbon Stocks of Northeastern China Using Expert Knowledge and GIS-based Methods

The main aim of this paper was to calculate soil organic carbon stock(SOCS) with consideration of the pedogenetic horizons using expert knowledge and GIS-based methods in northeastern China.A novel prediction process was presented and was referred to as model-then-calculate with respect to the variable thicknesses of soil horizons(MCV).The model-then-calculate with fixed-thickness(MCF),soil profile statistics(SPS),pedological professional knowledge-based(PKB) and vegetation type-based(Veg) methods were carried out for comparison.With respect to the similar pedological information,nine common layers from topsoil to bedrock were grouped in the MCV.Validation results suggested that the MCV method generated better performance than the other methods considered.For the comparison of polygon based approaches,the Veg method generated better accuracy than both SPS and PKB,as limited soil data were incorporated.Additional prediction of the pedogenetic horizons within MCV benefitted the regional SOCS estimation and provided information for future soil classification and understanding of soil functions.The intermediate product,that is,horizon thickness maps were fluctuant enough and reflected many details in space.The linear mixed model indicated that mean annual air temperature(MAAT) was the most important predictor for the SOCS simulation.The minimal residual of the linear mixed models was achieved in the vegetation type-based model,whereas the maximal residual was fitted in the soil type-based model.About 95% of SOCS could be found in Argosols,Cambosols and Isohumosols.The largest SOCS was found in the croplands with vegetation of Triticum aestivum L.,Sorghum bicolor(L.) Moench,Glycine max(L.) Merr.,Zea mays L.and Setaria italica(L.) P.Beauv.

Fault-free Hamiltonian cycles passing through a prescribed linear forest in 3-ary n-cube with faulty edges

The k-ary n-cube Qkn （n ≥2 and k ≥3） is one of the most popular interconnection networks. In this paper, we consider the problem of a fault- free Hamiltonian cycle passing through a prescribed linear forest （i.e., pairwise vertex-disjoint paths） in the 3-ary n-cube Qn^3 with faulty edges. The following result is obtained. Let E0 （≠θ） be a linear forest and F （≠θ） be a set of faulty edges in Q3 such that E0∩ F = 0 and ｜E0｜ ＋｜F｜ ≤ 2n - 2. Then all edges of E0 lie on a Hamiltonian cycle in Qn^3- F, and the upper bound 2n - 2 is sharp.