Almost resolvable k‐cycle systems with

Abstract

In this paper, we show that if k≥6 and k≡2(mod4), then there exists an almost resolvable k‐cycle system of order 2kt+1 for all t≥1 except possibly for t=2 and k≥14. Thus we give a partial solution to an open problem posed by Lindner, Meszka, and Rosa (J. Combin. Des., vol. 17, pp. 404–410, 2009).

Hierarchical Microcables Constructed by CoP@C⊂Carbon Framework Intertwined with Carbon Nanotubes for Efficient Lithium Storage

“…Nevertheless, the practical use of these materials always suffers from rapid capacity fading during cycling because the irreversibility of the conversion reaction and the large volume changes during the conversion reactions. [9][10][11][12][13] Furthermore, the synthesis of phosphates is much more difficult than metal oxides or sulfides as phosphating process produces more or less toxic substances. To solve the series of problems, gigantic effort has been made.…”

On the Existence of a Cyclic Near-Resolvable (6n+4)-Cycle System of 2K12n+Aldiabat1, Ibrahim2, Karim3 2019Journal of Mathematics2020View full textAdd to dashboardCite

“…A near-resolvable -cycle system of V has been constructed for = 4 with V ≡ 1 (mod 8) except possibly values V = 33, 41, 57 and except V = 9 (for which such a system does not exist) [21], = 10 with V ≡ 5 (mod 20) or V = 41 [22], ≥ 11 with V = 4 + 1 [23]. Recently, the existence of a near-resolvable -cycle system of 2 +1 for all ≥ 1 and ≡ 2 (mod 4) except possibly for = 2 and ≥ 14 has been proved by Wang and Cao [24]. Previously, it has been proved that there exists a ( + 1, , 2)for all odd ≥ 3 and all ≥ 1 [25].…”