In this paper we give a Dirac type condition for heavy cycles in a 3-connected weighted graph, reading that if d^w（v）≥ d for all v ∈ V（G）／{x} and w（uz） = w（vz）, when uz, vz ∈ E（G） and uv ∈/ E（G）. Then...In this paper we give a Dirac type condition for heavy cycles in a 3-connected weighted graph, reading that if d^w（v）≥ d for all v ∈ V（G）／{x} and w（uz） = w（vz）, when uz, vz ∈ E（G） and uv ∈/ E（G）. Then G contains either an （x, y）-cycle of weight at least 2d or a Hamilton cycle.展开更多
A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The sum of the weights of the edges incident with a vertex v is called the weighted degree of v, denoted by dw（v...A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The sum of the weights of the edges incident with a vertex v is called the weighted degree of v, denoted by dw（v）. The weight of a cycle is defined as the sum of the weights of its edges. Fujisawa proved that if G is a 2-connected triangle-free weighted graph such that the minimum weighted degree of G is at least d, then G contains a cycle of weight at least 2d. In this paper, we proved that if G is a 2-connected triangle-free weighted graph of even size such that dw（u） ＋ dw（v） ≥ 2d holds for any pair of nonadjacent vertices u, v ∈ V（G）, then G contains a cycle of weight at least 2d.展开更多
After analysing the disadvantages of the traditional residue hydrotreating-catalytic cracking combination process, RIPP has proposed a bi-directional combination technology integrating residue hydrotreating with catal...After analysing the disadvantages of the traditional residue hydrotreating-catalytic cracking combination process, RIPP has proposed a bi-directional combination technology integrating residue hydrotreating with catalytic cracking called RICP which does not further recycles the FCC heavy cycle oil (HCO) inside the FCC unit and delivers HCO to the residue hydrotreating unit as a diluting oil for the residue that is concurrently subjected to hydrotreating prior to being used as the FCC feed oil. The RICP technology can stimulate residue hydrotreating reactions through utilization of HCO along with an in- creased yield of FCC light distillate, resulting in enhanced petroleum utilization and economic benefits of the refinery.展开更多
文摘In this paper we give a Dirac type condition for heavy cycles in a 3-connected weighted graph, reading that if d^w（v）≥ d for all v ∈ V（G）／{x} and w（uz） = w（vz）, when uz, vz ∈ E（G） and uv ∈/ E（G）. Then G contains either an （x, y）-cycle of weight at least 2d or a Hamilton cycle.
基金Supported by National Natural Science Foundation of China(Grant No.11001269)
文摘A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The sum of the weights of the edges incident with a vertex v is called the weighted degree of v, denoted by dw（v）. The weight of a cycle is defined as the sum of the weights of its edges. Fujisawa proved that if G is a 2-connected triangle-free weighted graph such that the minimum weighted degree of G is at least d, then G contains a cycle of weight at least 2d. In this paper, we proved that if G is a 2-connected triangle-free weighted graph of even size such that dw（u） ＋ dw（v） ≥ 2d holds for any pair of nonadjacent vertices u, v ∈ V（G）, then G contains a cycle of weight at least 2d.
文摘After analysing the disadvantages of the traditional residue hydrotreating-catalytic cracking combination process, RIPP has proposed a bi-directional combination technology integrating residue hydrotreating with catalytic cracking called RICP which does not further recycles the FCC heavy cycle oil (HCO) inside the FCC unit and delivers HCO to the residue hydrotreating unit as a diluting oil for the residue that is concurrently subjected to hydrotreating prior to being used as the FCC feed oil. The RICP technology can stimulate residue hydrotreating reactions through utilization of HCO along with an in- creased yield of FCC light distillate, resulting in enhanced petroleum utilization and economic benefits of the refinery.
