On the ｛P_2,P_3｝-Factor of Cubic Graphs

Ler G = （ V, E） be a finite simple graph and Pn denote the path of order n. A spanning subgraph F is called a { P2, P3 }-factor of G if each component of F is isomorphic to P2 or P3. With the path-covering method, it is proved that any connected cubic graph with at least 5 vertices has a { P2, P3 }-factor F such that｜P3（F）｜P2（F）｜, where P2（F） and P3（F） denote the set of components of P2 and P3 in F, respectively.

Optimization of mechanized soil covering path based on the agronomic mode of full-film double-ditch with double-width filming

In order to further improve the working performance and efficiency of mechanized tillage operation of a full-film double-ditch seedbed,under the working conditions of different parameters of the spiral push-type soil covering device with double-width filming,the dynamic soil covering characteristics and soil covering uniformity of the device were analyzed,the collaborative and interactive coupling mechanism of the horizontal pushing process of the mulching soil and horizontally two-way spiral soil transmission device were revealed,and the main reasons for the influence of different soil covering belts on the change of soil particle number distribution were analyzed.Based on the full-film double-ditch mode with double-width filming,the mechanized soil covering path was optimized.In order to further reduce the disturbance on mulching soil by two-way spiral pushing,a kind of parallel shunt type soil covering device with double-width filming was designed,then a discrete element method was adopted to make simulation analysis and optimize the parallel shunt type soil covering device with double-width filming.Field verification tests showed that after the operation of the full-film double-ditch combined machine with double-width filming and soil covering installed with the parallel shunt type soil covering device,the qualified rate of the film edge soil covering width was 96.1%,an increase of 1.6%compared to that before optimization;the qualified rate of soil covering width at the center of the big ridge was 93.5%,an increase of 1.9%compared to that before optimization;the qualified rate of the soil covering thickness was 97.7%,an increase of 0.2%compared to that before optimization.The test indicators reached the requirements of relevant national and industrial standards,showing that the test results met the design requirements,and the working conditions of verification tests were consistent with the simulation results.