For an integer , a graph is -hamiltonian if for any vertex subset with , is hamiltonian, and is -hamiltonian connected if for any vertex subset with , is hamiltonian connected. Thomassen in 1984 conjectured that every 4-connected line graph is hamiltonian (see Thomassen, 1986), and Ku?zel and Xiong in 2004 conjectured that every 4-connected line graph is hamiltonian connected (see Ryjá?ek and Vrána, 2011). In Broersma and Veldman (1987), Broersma and Veldman raised the characterization problem of -hamiltonian line graphs. In Lai and Shao (2013), it is conjectured that for , a line graph is -hamiltonian if and only if is -connected. In this paper we prove the following.(i) For an integer , the line graph of a claw-free graph is -hamiltonian if and only if is -connected.(ii) The line graph of a claw-free graph is 1-hamiltonian connected if and only if is 4-connected. 相似文献
To establish a new method of testing and evaluating the quality of refined montan wax (RMW), digital color and GC fingerprint technology were introduced and applied. CIE Lab color mode was used to digitize the exterior colors of RMW, and the score obtained through a fitting function was also used to reflect its quality. It is shown that they were in complete accord with the human visual perception trend. The GC fingerprint was used to characterize the internal chemical information of RMW, and the composition of its internal features was reflected through the relative retention time (RRT) and relative peak area (RPA) values. It is shown that there was a high degree of similarity between the fingerprints, while certain differences also existed. This can be used to implement effective application of RMW to aspects such as quality control, adulteration identification, and origin attributions.
Highly strained quantum cascade laser (QCL) and quantum well infrared photodetector (QWIPs) structures based on InxGa(1−x)As−InyAl(1−y)As (x>0.8,y<0.3) layers have been grown by molecular beam epitaxy. Conditions of exact stoichiometric growth were used at a temperature of 420°C to produce structures that are suitable for both emission and detection in the 2–5 μm mid-infrared regime. High structural integrity, as assessed by double crystal X-ray diffraction, room temperature photoluminescence and electrical characteristics were observed. Strong room temperature intersubband absorption in highly tensile strained and strain-compensated In0.84Ga0.16As/AlAs/In0.52Al0.48As double barrier quantum wells grown on InP substrates is demonstrated. Γ–Γ intersubband transitions have been observed across a wide range of the mid-infrared spectrum (2–7 μm) in three structures of differing In0.84Ga0.16As well width (30, 45, and 80 Å). We demonstrate short-wavelength IR, intersubband operation in both detection and emission for application in QC and QWIP structures. By pushing the InGaAs–InAlAs system to its ultimate limit, we have obtained the highest band offsets that are theoretically possible in this system both for the Γ–Γ bands and the Γ–X bands, thereby opening up the way for both high power and high efficiency coupled with short-wavelength operation at room temperature. The versatility of this material system and technique in covering a wide range of the infrared spectrum is thus demonstrated. 相似文献