Let Pt and C` denote a path on t vertices and a cycle on ` vertices, respectively. In this paper we study the k-coloring problem for (Pt, C`)-free graphs. Maffray and Morel, and Bruce, Hoang and Sawada, have proved that 3-colorability of P5-free graphs has a finite forbidden induced subgraphs characterization, while Hoang, Moore, Recoskie, Sawada, and Vatshelle have shown that k-colorability of...

Abstract In this paper, the KdV-Sawada-Kotera-Ramani(KdVSKR) equation in various dimensions are studied. The bilinear form of (1+1)-dimensional and (2+1)-dimensional KdVSKR obtained by independent transformation. Based on Hirota method, we constructed new interaction solutions studying unknown nonlinear differential equations for corresponding parameters. Three dimensional plots, density plots ...

Phospholipidosis (PLD) is characterized by an intracellular accumulation of phospholipids in lysosomes and the concurrent development of concentric lamellar bodies. Recently, H. Sawada et al. (2005, Toxicol. Sci. 83, 282-292) identified 17 genes as potential biomarkers of PLD in HepG2 cells. The present study was undertaken to determine if this set of genes measured by quantitative PCR could be...

By N -soliton solutions and a velocity resonance mechanism, soliton molecules are constructed for the KdV-Sawada-Kotera-Ramani (KSKR) equation, which is used to simulate resonances of solitons in one-dimensional space. An asymmetric can be formed by adjusting distance between two molecule small enough. The interactions a...

We study how to generate binary de Bruijn sequences efficiently from the class of simple linear feedback shift registers with function $f(x_0, x_1, \ldots, x_{n-1}) = x_0 + x_1 x_{n-1}$ for $n \geq 3$, using cycle joining method. Based on properties this LFSRs, we propose two new generic successor rules, each which produces at least $2^{n-3}$ sequences. These classes build upon a framework prop...