World-wide increased energy consumption and demand has aimed our prime requisites of high-energy storage systems with longer life. Hence, research and development on supercapacitors based on efficient and robust electrode...

For a family of graphs F, the F-Contraction problem takes as an input a graph G and an integer k, and the goal is to decide if there exists S ⊆ E(G) of size at most k such that G/S belongs to F. Here, G/S is the graph obtained from G by contracting all the edges in S. Heggernes et al. [Algorithmica (2014)] were the first to study edge contraction problems in the realm of Parameterized Complexity. They studied F-Contraction when F is a simple family of graphs such as trees and paths. In this paper, we study the F-Contraction problem, where F generalizes the family of trees. In particular, we define this generalization in a "parameterized way". Let T be the family of graphs such that each graph in T can be made into a tree by deleting at most edges. Thus, the problem we study is T -Contraction. We design an FPT algorithm for T -Contraction running in time O((2 √ + 2) O(k+ ) · n O(1) ). Furthermore, we show that the problem does not admit a polynomial kernel when parameterized by k. Inspired by the negative result for the kernelization, we design a lossy kernel for T -Contraction of size O([k(k + 2 )] ( α α−1 +1) ).

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Summary Factual realization of 2‐fold material mutualistic approach has been demonstrated as a state‐of‐art for the growth of copper phosphate (Cu2P2O7) microflowers on multi‐walled carbon nanotubes (MWCNT) through simple, low cost, and industry‐scalable chemical route, namely, successive ionic layer adsorption and reaction. Rationally designed unique surface architecture synergistically comprehends the merits of highly conductive electric double‐layer capacitance‐based MWCNT skeleton and pseudocapacitance enriched Cu2P2O7 enabling Cu2P2O7/MWCNT (CuCNT) composite. As‐synthesized CuCNT electrode exhibits reciprocity toward exceptionally enhanced electrochemically active surface area of 398.6 m2 g−1, high specific capacitance of 465 F g−1 at 13 A g−1, and extraordinary cyclic stability. Comparative accounting of charge storage in terms of surface‐capacitive and diffusion‐controlled mechanisms has been explored in depth to gain insight into internal electrochemical kinetics. Furthermore, symmetrically configured bendable solid‐state supercapacitor device using CuCNT delivers proficient specific energy of 25.4 Wh kg−1 together with high mechanical stability of 96% at 170° of bending. Also, the experimentally and theoretically evaluated series and parallel combination of two devices serve as a showcase toward potential candidature for applications of specific requirements. Furthermore, live demonstration through lightening of 21 red light‐emitting diodes authorizes the probable commercialization of the present CuCNT device.